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The hosts needed an extra-time winner from James Troisi to see off South Korea in the final and claim their first piece of major silverware after a gripping contest at Stadium Australia.
Clearly their coach has no intention of resting on his laurels, targeting a significant improvement on a winless Brazil 2014 when the team in green and gold next find themselves on FIFA's big stage.
"We want to go to the next World Cup and make an impact," he said.
"I'm not going to put any limits on what they can achieve.
"The goal for this confederation should be to break the European-South American monopoly on the World Cup. That may sound farfetched but it's got to be the goal. We have to contribute to that."
Postecoglou hailed the character of his team, who managed to bounce back during the additional 30 minutes after conceding Son Heung-min's body-blow of an equaliser in injury time in Sydney.
"It would have broken a lot of teams," he said.
"We knew we were still going to be strong. We knew we had them on fitness. It just a question of making sure they refocused."
Attention quickly turned after the match to the future of veteran talisman Tim Cahill, with speculation mounting over whether or not the 35-year-old will now choose to end his international career on a high.
"I'd be surprised ... he hasn't said anything to me," Postecoglou said.
"I haven't had any discussions with him about his future and I'd be surprised if I had to. Because he's a very important part of our team."
The victorious coach also paid a fitting tribute to his team's vanquished opponents, the Taeguk Warriors having contributed fully to a memorable encounter.
"Credit to Korea," he said.
"The two best sides were playing off for the trophy and it was a game worthy of producing a champion."