The Socceroos dominated Oman in their second group game after a scorching opening 45 minutes to qualify for the quarter-finals with one game left in the group.
Three goals before the break all but sealed the result with Matt McKay, Robbie Kruse and Mark Milligan on the scoresheet, before substitute Tomi Juric made it four after the break in front of over 50,000 fans at Stadium Australia.
But Postecoglou only has eyes for improvement as the green and gold head to Brisbane for their final group match against South Korea.
"We went up another level tonight, as we expected. And we expect to improve as we go through the tournament," he told reporters.
"And we still have improvement in us, and from my perspective I'll be emphasising to the players that what they've done so far has been good, but we certainly can get better."
Juric’s neat finish made it eight different scorers for the Socceroos in their first two games of the tournament following Saturday’s 4-1 defeat of Kuwait in Melbourne.
"It just shows the even contribution of the team and the way the players have embraced the way we want to play, we have multiple threats,” said Postecoglou.
"The way we play makes it very hard for the opposition. We made three changes tonight and we made some early substitutions but as you saw the team didn't miss a beat."
Postecoglou also provided an update on the fitness of captain Mile Jedinak, who missed the clash with Oman with an ankle problem.
"We'll assess that as we go, he's no certainty for the Korea game," he said.
"It's nothing major, nothing that will keep him out for a length of time but obviously with games backing up pretty quickly - from our perspective we made the decision early that he's not available for [the match against Oman].
"Mile's pretty keen to play obviously and if he's anywhere near fit he will play, but at this stage we're just taking it day by day."
