Postecoglou and his players lamented the playing surface at Sydney's Olympic Stadium on Saturday night after Australia defeated Greece 1-0 in a friendly courtesy of a late Mathew Leckie strike.
The pitch, which had hosted a rugby league match on Wednesday, was cleared for play by the match referee despite the deluge of rain that fell on Sydney throughout Saturday.
Greece-born Postecoglou said he felt "embarrassed" about the conditions.
"We've got an international team here that we're hosting and we're supposed to be the sporting nation of the world," he told reporters.
"The crowd were fantastic (but) I felt sorry for them ... it's just not good enough.
"I can tell you what the Greek players were saying when they were coming off the pitch, and they're too polite to say anything publicly.
"We have world-class venues, world-class atmospheres, our supporters are second to none -- we love our sport.
"But in our game and our game alone, the pitch is actually an essential part of the spectacle.
"If that's not good then we're cheating people."
Australia kick off the next round of Asian qualifying for the 2018 World Cup in Russia with a home game against Group B rivals Iraq on Sept. 1 and host regional heavyweights Japan the following month.
Postecoglou said scratchy home pitches were hindering his team's ability to play good football, which could have consequences for their hopes of reaching Russia.
"Our whole World Cup qualification could hinge on it," said the 50-year-old.
"Do we not want the conditions to suit us? To present a pitch that suits our style of game to get that advantage?
"I'm sure when we play in Japan they will, so we shouldn't have to prove we're some sort of pedigree before we get what I think our nation deserves."
(Reporting by Ian Ransom; Editing by Nick Mulvenney)
