It marked a fifth consecutive defeat for the champions.
Postecoglou said afterwards: "Proud of the lads. To come to City at their place is a daunting prospect. It challenges every part of you. A bit of everything today. We had to be disciplined and work hard - and play decent football - and we did that. Our football was the difference today.
"Outstanding performance.
"You have to be (clinical). They won't give you too many opportunities. There was a calmness and maturity about how we handled the ball. Against City you can get spooked and don't want to play against them. But you have to play.
"They test you in every way - mentally, physically, tactically. Our flat spots have been really flat and something we need to eradicate. We're a much better team this year than last year. We just need to find consistency."
On two-goal James Maddison, he said: "Not just the goals. He was going to be key for us in getting control of the midfield. He worked hard defensively. He's gone through a bit of a lean spell but he's stayed with us during the international break. He was determined to get back to the levels he wants to be. It was a perfect game for him.
"He hasn't been that badly out of form. He just sets high standards. Part of that is on me - I have to get the best out of the players."
On his centre-backs, he also said: "Brilliant. Ben and Radu were outstanding and Vicario when we needed him. Those two, not just defensively, a part of it was playing out from the back and they had to get on it first. They showed courage and got the rewards.
"I haven't sensed like we've lost belief. We've just been disappointed in a couple of games when we haven't reached the levels.
"I don't dismiss today. it's significant. The other four losses were away."