The Socceroos led 1-0 in the 91st minute before the Koreans equalised with just two minutes remaining of regulation time.
But Australia prevailed in a tense extra-time courtesy of substitute James Troisi’s winner in the 105th minute.
Asked his main emotion, Postecoglou replied: “It’s a funny one.
“Probably relief is the biggest one because you see so many people work so hard, and the players work so hard, and you want them to get the rewards.
“I have been around long enough to know this game is pretty cruel sometimes.”
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But Postecoglou’s faith never wavered.
“I really believed in the whole group – the players, the staff – that there was a resilience in them,” he said.
“I said it to them during the day, whatever was going to happen today, and I knew that it wouldn’t just run to script or be simple, they had the power within them to overcome it.
“To see so many happy faces, you just get relief.”