Postecoglou's side beat Liverpool 2-1 last Saturday after the Reds had a Luis Diaz goal wrongly disallowed for offside in the first half.
Diaz's strike would have put Jurgen Klopp's men ahead, but VAR operator Darren England mistakenly believed the on-field decision had been to award the goal.
After establishing that Diaz had been onside, England told the match officials the check was complete and the game restarted, but in fact the goal was originally ruled out for offside and the score stayed at 0-0 following the miscommunication.
Referees body the Professional Game Match Officials Limited admitted it was a "significant human error", with Klopp claiming a replay was the fairest solution for his team in the aftermath of Joel Matip's decisive own goal in stoppage time.
There is no suggestion of a replay being considered by Premier League chiefs, but Postecoglou was willing to admit his side had a lucky break.
"The facts of it are that it was a legitimate goal Liverpool scored that wasn't given," the Australian told reporters on Friday.
"You kind of look at why it's not given because that's the first thing you question: obviously something has broken down.
"It became clear it wasn't an integrity issue. It wasn't a misappropriation of the law. It was an error in communication, a mistake, a mistake which cost Liverpool.
"I get that it's an unusual one in that it's never happened before, but at the same time we're in a new space anyway with technology where I think they'll be a lot of firsts with the way we deal with these things."
Postecoglou pleaded for understanding to be shown towards VAR official England.
"It's a significant error but it's a human being that's made that error," he said on the eve of his side's trip to Luton. "I don't think that there's anything that needs to go too far-reaching.
"I hope that's what they're addressing, not the individual that made the mistake. I think that's a dereliction of the game.
"That's like me hanging out a player to dry just because he made a mistake. My role is to go in and help that player to improve not say 'now you're never playing again'."
