They sit 11th in the English Premier League table, winning just seven of their opening 19 league fixtures.
Postecoglou left Celtic to take the managerial role at Spurs on June 6, 2023, penning a four-year contract.
At Celtic, the 59-year-old won successive Scottish Premiership titles during his two seasons in charge.
But there's now pressure on Spurs chairman Daniel Levy to make a decision on the Greek-Aussie's future in north London.
During his post-match press conference, Postecoglou insisted that he will “keep going”.
“We’re asking a lot of a small core group of players,’ he explained.
“The whole group probably needs a couple of days to get away and recover.
“It has been really intense for a core group of players. It will do them good to go away with their families to recover with their families mentally as much as physically.
“I will keep going and look for help to get these players to perform at their best.”