Postecoglou's side drew 1-1 with Rangers in the Europa League, meaning the Scottish club are still yet to beat an English Premier League club in European competition since November 1992.
It was Rangers who struck first in the 47th minute as Hamza Igamane lashed home an inviting cross by James Tavernier from the right.
However, Tottenham's Dejan Kulusevksi ensured the visitors would leave Ibrox with a point when he scored 15 minutes before the end.
Kulusevski began the contest on the bench but was thrown on at the start of the second half.
The Swede came on in place of Timo Werner, who was largely ineffectual for the opening 45 minutes and gave Postecoglou little reason to keep him on.
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Postecoglou didn't mince his words on Werner's performance and he certainly let the German know it.
"He wasn't playing anywhere near the level he should," Postecoglou said in his post-match press conference.
"When you've got 18-year-olds it's not acceptable to me. I said that to Timo. He's a senior international, he's a German international.
"In the moment we're in right now, it's not like we've got many options. I need everyone to at least be going out there trying to give the best of themselves.
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"His performance in the first half wasn't acceptable."
Postecoglou added: "We need everybody including him to be contributing, because we don't have the depth to leave people out if they're performing poorly.
"We need them to play their part. Especially the senior guys. When I'm asking younger guys to do massive jobs.
"I expect a level of performance from some of the senior guys and today wasn't that."
Werner's blank against Rangers meant his goal tally this season remained at just one from 19 appearances across all competitions.
It was far from a perfect performance from Tottenham, whose defensive issues were exposed once more.
In fact, Igamane's strike ensured Postecoglou's side had kept just one clean sheet from their last 11 games.
Rangers also finished the contest with more shots and shots on target than their Premier League counterparts despite having 41 per cent possession.
The display, especially defensively, left former Tottenham player Jamie O'Hara feeling like he's 'had enough'.
"My patience is wearing thin," O'Hara said on The Sports Bar.
"Patience is wearing thin. Ange Postecoglou, mate. I've had enough.
"You know, we go on and like, oh yeah, the football's great. Is it? Is it great?
"I'm not watching Barcelona. I'm just watching a good team, you know, in moments, have some decent spells, but you know, every team plays good football.
"It's not like I'm watching Barcelona play, but can't defend, but when we've got the ball, it's just, you know, it's brilliant to watch. All I'm watching is a Tottenham team that I've watched a million times before. Boring.
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"There's nothing special."
Postecoglou will hope Tottenham's winless run doesn't stretch to a sixth game on Sunday as they travel to lowly Southampton.