Lucas Bergvall struck late for the 1-0 win on Wednesday night.
Postecoglou said afterwards: "We are having to deal with adversity all the time. We started really well and then lost a key player. This lot are nothing if not resiliant and they keep going and they did today.
"It is incredible when you think we had a couple of 18-year-olds out there. I have just seen so much growth. I have no doubt we will get through this period and get players back, what I've found in the meantime is we have some real players to help us to be the team we want to be."
On goalkeeper Antonin Kinsky making his debut, he said: "That is a big occasion for a young man. He handled himself outstandingly."
He continued: "It is only half-time and going to Liverpool is not easy but just that feeling of having a victory against a really strong opponent I want the players to feel good about it.
"People can keep mocking me about it (winning a trophy) but we will see."