After James Maddison was fouled by Frankfurt goalkeeper Kaua Santos, Solanke converted from the spot to seal a 1-0 win against the Bundesliga side and a spot in the Europa League semi-finals against Bodo/Glimt next month.
It was the England international's first goal in 12 games but that did not stop Postecoglou who has hailed the 27-year-old as he prepares to find the net once more against Forest.
"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."
Richarlison is fit after recovering from a calf injury and could start on Monday night for the first time since early February. Postecoglou teased his return and suggested that the Brazilian international could make an impact.
"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.”