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Tottenham boss Thomas Frank has apologised to fans for their dismal 4-1 defeat at Arsenal, as Spurs goalkeeper Guglielmo Vicario admitted they showed no fight against their north London rivals.

Spurs' wretched loss saw them produce the lowest expected goals by any team in a Premier League match so far this season, with their 0.07 xG surpassing their previous record-low of 0.12 xG registered in their 1-0 home defeat to Chelsea at the start of November.

Just 22 days on, Spurs slumped to another abysmal defeat as they slipped to ninth in the table, having won just three of their last 11 games in all competitions.

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The meek defeat at the home of their local rivals was labelled "embarrassing" by ex-Spurs striker Les Ferdinand, forcing Frank to say sorry to the club's fans.

The Dane told Sky Sports: "It's extremely painful. It was a bad performance and completely the opposite of what the intention was before we came here.

"We can only apologise to the fans for this performance.

"No matter if the team went to play a bit short, they got on top of that, and we couldn't get out.

"They were stronger in the duels and we couldn't get out of those duels. When it went long, with the duels and second balls, we didn't win enough of those.

"On the day, a bad performance that we lost.

"I've seen a lot of fight and character in this team [in the past] but one big thing we didn't do well enough was winning the duels.

"We can call that whatever we want to call it, but we didn't win enough duels."

He added in his post-match press conference: "It's fair to say that we are very disappointed and unhappy with the performance today. I don't want to run away from that.

"As I said, I apologise to the fans. I think it's also fair to say where we're coming from - we finished 17th last year, and we're trying to build something, which today didn't look like we tried to build something."

Vicario: We didn't fight

Spurs suffered a fourth successive defeat against Arsenal, with the Gunners' 4-1 win their joint-biggest Premier League victory over them.

Vicario, a member of Tottenham's leadership group under Frank, also apologised to fans and criticised the team's fight in the loss as they now turn their attentions to another tough task, as they visit Champions League holders Paris Saint-Germain on Wednesday.

"It was a very bad night for us," the Italian told Sky Sports. "First of all, we have to apologise to the people that support us and travel, to expect to watch a fight because as a collective, we didn't fight.

"That's not negotiable to compete in a football match, especially at this level.

"But now is a tough night, it's a very bad defeat, but we have to stick together because we know what we have to address.

"We have another big night on Wednesday. We have to stick together and believe in ourselves because tonight we didn't show anything that we're normally capable of.

"I know the emotions are high when you lose a derby like that, but we need to have cool heads."

Ferdinand agreed with Vicario over the lack of grit shown in the defeat.

He said: "It wasn't a five-star performance from Arsenal. The scoreline was five-star, but there was no fight. Arsenal didn't get out of third gear.

"You expect a little bit of spark. Arsenal have got three players who haven't played in a north London derby before. Tottenham probably had one. But there was nothing.

"At the start of the week, I was thinking about this game. Nothing the players did out there felt like a north London derby."

Frank's tactics in spotlight

Frank opted to play a 5-4-1 system at Arsenal, but it backfired as the home side dominated the first half, scoring twice, while Spurs failed to have a shot at goal.

It led Frank to change to a 4-2-3-1 system at half-time, but Arsenal's hat-trick hero Eberechi Eze scored his second just 35 seconds after the restart.

Asked whether he got his tactics wrong at his post-match press conference, Frank said: "I always take full responsibility. So the full responsibility will always be on me. Today, when we didn't perform, I picked a team that played 5-4-1.

"I changed it at half-time. Very, very clever. One minute into it, they scored to make it 3-0, and then the rest is history after that.

"What I would say is that no matter if you played one or another system, we needed to be more aggressive and be better than the duels - that doesn't matter what system.

"But I take the responsibility for everything today."

Jamie Carragher believes ex-Brentford boss Frank needs to be more positive if he is to be a success at Spurs.

He told Sky Sports: "The one negative so far under Thomas Frank is can he go from being a pragmatic coach and trying to make it difficult for the opposition, as he tried to do here, to more about how are they going score? How are they going to win a game?

"I can keep going back to the underlying numbers and the xG. It's very low.

"Even after watching the first five minutes of the game you're thinking 'what are Tottenham going to do here to hurt Arsenal?'

"That is the problem with every manager making a jump to a top team. You've got to have more than just trying to stop the opposition. That's not having a go at Thomas Frank. The top managers are there for a reason.

"They are special, they are elite. It's because they can coach teams to be difficult to beat at times, but also they can coach teams to win games. That is the big difference. If you don't get that right, you won't be in a job that long."

Tottenham were close to signing Eberechi Eze during the summer but they could not get near him at the Emirates Stadium. This was a brutal exhibition of what they missed out on, performed by a man seemingly on a mission to hammer home the message.

Thomas Frank had tried to make light of facing him. "Who's Eze?" he joked in his pre-match press conference. But Eze was determined to make his mark and did so in historic style, becoming the first Arsenal player since 1978 to score a hat-trick in a north London derby and inspiring the Gunners to a thumping 4-1 win.

"It's special," he smiled to Sky Sports afterwards. "It's what I prayed for. I prayed for my hat-trick and I got it." But this was more than divine intervention. Mikel Arteta revealed Eze had cut short a day off in the lead-up to the game, such was his determination to be ready.

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"Things happen for a reason," said the Arsenal boss. "After the international duty, he had two days off and, after one day, he wanted to train and he wanted to improve and he wanted to do extra practice. He was asking me questions about this and that.

"When a player has such a talent and his desire is at that level, then these things happen."

His desire to make an impact was clear from as early as the third minute of the game, when he put Declan Rice in on goal with a delightful, clipped pass. Rice wasted the opening, sending his shot too close to Guglielmo Vicario. Eze would make no such mistake.

His first goal, when he made space in a crowded Spurs box, too quick for Rodrigo Bentancur and Joao Palhinha, before slamming a low finish through more white-shirted defenders, was a perfect example of the qualities that made him so attractive to Arsenal.

Eze has the technical skill to find room even in the tightest spaces and never passes up an opportunity to shoot. "Yeah, and it doesn't have to be perfect," smiled Arteta afterwards. "He can be right, left, ball on the ground, bouncing, ball at this height and he takes it. He has such a quality and capacity to finish actions in different ways."

Eze demonstrated the same qualities for his second and third goals, only the finishes got even better. After finding the corner in ruthless style from Jurrien Timber's square ball, he allowed a desperate Destiny Udogie to slide past him before dispatching Leandro Trossard's pass, this time into the other corner of the net.

That goal sent him home with the matchball and capped a masterful individual performance. Eze has looked inhibited at times since his arrival at Arsenal from Crystal Palace but this was not one of them. He plays with a level of directness untypical among his team-mates and clearly that is not all that sets him apart.

"Since the day that he came, he has brought something else to the team, a certain joy, a certain aura that this team needed," added Arteta in his press conference afterwards. "Hopefully it will give a lot of confidence to him and the team.

"At any moment he can win us a game and that's the ability that he has and he certainly needs to fulfil that talent."

He is doing that now. But it all started with a phone call to Arteta when he was on the verge of joining Spurs. "When he picked up the phone last summer, I remember he said he wanted to play for us and he wanted to be part of this team. You can really sense that."

He was helped by a role which gave him freedom against Spurs.

With Martin Odegaard still absent as he recovers from injury, Eze started, again, in the No 10 position, although encouraged to interchange positions with makeshift striker Mikel Merino.

"He finds a way to be in and around the box," said Arsenal legend Thierry Henry on Sky Sports. "He didn't have a proper No 9 to play and that's why I think it was easier for him to get in the box, because you don't have the presence of a No 9. He was a No 9 at times."

He relished the opportunity. In addition to scoring three goals, Eze finished the game having had more shots and more touches in the opposition box than any other player, with six and seven respectively, his focus on inflicting maximum damage.

It was by far his best performance yet for Arsenal but it also hinted at how much more there is to come from him.

"When Eze came in, I thought, okay, maybe it's not a game-changer," said Sky Sports pundit Jamie Carragher after the match.

"But then we saw some of his highlights this season, there were still a few great goals in there, and then he goes and scores a hat-trick. So, apologies. I certainly undervalued the importance of that signing because he looks like he could make the real difference for Arsenal this season and going on to win the title."

That is the hope for Arsenal now, six points clear at the top and, thanks in part to the addition of Eze, and the "aura" shown against Spurs, looking every bit like a side capable of winning the prize.

Neville: Arteta getting the balance right

Sky Sports' Gary Neville on Arsenal:

"Over the last few years, Arsenal have been building towards trying to win a title, they haven't won one yet, but they do a lot of things very well. The narrative going into this game was Gabriel's injury, but no one is interested anymore because they have got a squad that can cope without players being fit.

"We've seen Hincapie slot in really naturally, Mosquera has done it previously, so that narrative won't build.

"Tottenham were a team waiting to get beaten. After what happened with Liverpool and Man City yesterday it was a much-needed victory, and they have sent a message to everyone in the league.

"It's a squad that should win the Premier League and go on to win the Champions League in the next two or three years. It might not be this season, but they are getting to that level of consistency and stability. The squad are pushing each other. Eberechi Eze looked Brazilian, it's beautiful to see that confidence from an English player.

"I've accused Mikel Arteta of being a bit handbrake on, but he's now getting that balance right of flair in the team and confidence, it's the intent - don't pass sideways, you're better than that. Their open-play game was really good, which they've been accused of lacking. A lot to like."

Eberechi Eze scored a sensational hat-trick as Arsenal moved six points clear at the top of the Premier League with a 4-1 thrashing of north London rivals Spurs at the Emirates Stadium.

Eze, who came close to joining Spurs before his move to Arsenal in August, showed them what they missed out on as he produced three outstanding finishes after Leandro Trossard's opener in a masterful performance in his first north London derby.

Spurs briefly threatened an unlikely comeback when Richarlison beat David Raya with an audacious lob from 35 yards out, but Arsenal were already three up at that point and Eze's hat-trick goal, curled brilliantly beyond Guglielmo Vicario, killed the game.

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Richarlison's goal was one of only three shots by Spurs, who switched to a back five but could not resist Arsenal's dominance, with Eze guiding his first goal into the bottom corner following smart footwork after Mikel Merino had picked out Trossard for the opener.

Thomas Frank reverted to a back four at half-time, throwing on Xavi Simons for Kevin Danso, but Eze struck his second just 35 seconds after the restart, again picking out the corner in sublime style.

His hat-trick goal, following Richarlison's extraordinary strike for Spurs, was the pick of the three, making him only the fourth Arsenal player in history to score a treble against Spurs and making it four consecutive wins in the fixture for the Gunners.

With Manchester City and Liverpool having suffered defeats to Newcastle and Nottingham Forest on Saturday, Mikel Arteta's side open up a six-point gap on second-placed Chelsea, who they face live on Sky Sports at Stamford Bridge next Sunday.

The result emphatically ends Spurs' unbeaten start in Premier League away games under Frank, leaving them ninth as the head coach faces more questions about their lack of attacking threat.

Their total of just 0.07 expected goals against Arsenal was the lowest by any side in a Premier League game this season.

WATCH: All the goals!

Arteta hails 'special day' for Arsenal

Arsenal boss Mikel Arteta to Sky Sports:

"I enjoyed every minute of it - the preparation since they came back from the international break, the energy that I felt, the hunger to play the game, the enthusiasm, the joy.

"And when you play in the manner we played and to win with the goals we scored against our rivals always makes it a special day.

"We want to impose ourselves in every department, but it starts with the intensity, with the duels, being very precise because the space is limited, there's a lot of aggression. They're a really good team and we have to earn it.

"From the beginning, we were really strong, really intense and we had to be patient. But we looked dominant, and scored two goals in the first half.

"In the second half, we maintained the consistency and even though there are things to improve, overall it was a great performance."

Eze: I prayed for my hat-trick

Arsenal's Eberechi Eze speaking with Sky Sports:

"That was a good one. Enjoyable day. Happy to help the team and get the win.

"It's special. It's what I prayed for. I prayed for my hat-trick and I got it.

"All my family are here which makes it more special to do it in front of them."

On potentially being a Tottenham player had the summer worked out differently.

"Let's not talk about that."

Frank: We can only apologise to our fans

Tottenham boss Thomas Frank to Sky Sports:

"It's extremely painful. It was a bad performance and completely opposite to what the intention was before we came here. We can only apologise to the fans for this performance.

"No matter if the team went to play a bit short, they got on top of that and we couldn't get out.

"They were stronger in the duels and we couldn't get out of those duels. When it went long, with the duels and second balls, we didn't win enough of those. On the day, a bad performance."

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