"I know he’s a striker and when they don’t score people will focus on that but he’s such an important part of the way we play," the Spurs head coach said ahead of Monday's Premier League game against Nottingham Forest.
"Our back four, five were outstanding [in Frankfurt] but our front three were so disciplined also in their defensive work on Thursday. Dom and the two wingers had important jobs for us from a defensive point of view.
"You ask them to do such a massive physical load and then they still have to produce when the ball gets up to them in an attacking sense.
"And maybe in other teams… if you look at Frankfurt, they don’t ask that of [their No.9, Hugo] Ekitike. When he gets the ball, he feels fresh and he can run at people.
"Dom usually receives the ball when he’s done four or five sprints closing people down so you factor that into it. But we feel as a team that gives us a better chance of success."
With Spurs captain Heung-min Son missing through injury, Postecoglou signalled for Solanke to take the penalty after James Maddison was clattered by Frankfurt goalkeeper Kaua Santos late in the first half, and the 27-year-old finished coolly before celebrating in front of Frankfurt's ultras behind the goal.
"I was delighted for him," added Postecoglou. "He took his penalty really well. Don’t underestimate the pressure he was under in that moment, taking a penalty away in Europe knowing how significant it is, right in front of the most vocal part of their fanbase. It shows the measure of the guy. He didn’t miss a beat.
"Important goal for us, important player for us, and we missed him when he was out. And when he was out and Richy was out, that was a big hole in our team."
Richarlison is fit after recovering from a calf injury and could start on Monday for the first time since early February, likely in place of Solanke.
"Richy is another one who is going to get some game time in the next couple of games because he's looking really good in training. But Dom’s been super important," Postecoglou said.
Spurs' focus is now firmly on a first European semi-final since 2019 but Postecoglou says they must pick up in the league, with his side slumped in 16th ahead of the visit of Champions League-chasing Forest.
"100 per cent. When we've got everyone fit, we believe we can beat anyone," he said. "Not many games left so another step closer, so hopefully we can go onto do it.
"This cup was something we had our eyes on from the start of the season. We're not far off it now so hopefully we can keep producing these performances in the cup and league throughout the rest of the season and kick on.
"We all know we need to be more consistent from game to game. When you have a game like this, you need to go out there and show no fear and get the job done. There's no second chances in knockout football so we knew we had to go and get the job done and that's what we did."