Prior to Spurs' match against Southampton on Sunday, Postecoglou doubled down on his negative comments regarding Timo Werner's performance against Rangers.
During the Europa League tie, the German lost possession 16 times, won none of his five duels and only completed 69 per cent of his passes.
That performance saw him substituted at half time for goalscorer Dejan Kulusevski - and Postecoglou didn't hold back in his assessment of Werner post-match.
The Aussie said that Werner's display was 'not acceptable' because he expects a certain 'level of performance from some of the senior guys'.
On Friday, when asked if Werner will be recalled at Saints, Postecoglou said: "I've got no choice. Who else am I going to play? I'm pulling kids out of school, I literally am.
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"That was the reasoning for me pointing it out last night. We need Timo. We need all of them.
"In normal times if you have a poor game, there's a price to pay. It doesn't exist right now. We need everybody we've got."
Responding to Postecoglou's comments, ex-Chelsea and West Ham striker Cole questioned how the Spurs players will respond to such public criticism of their teammate.
Cole told the Sports Bar Weekender on talkSPORT: "If it's that obvious, you go and tell him because now it's an insult to you and his teammates.
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"If you pander to the to the media first, before you've gone and told the player, and then the other players hear it in the press… you will lose the dressing room.
"Because now the players don't don't feel that you'll protect them when it's tough.
"I understand what he's saying and he's got every right to say it. But go say it to him.
"Because let's have it here… Werner is not his star player. So why are you picking on him? What about the others?
"What is he trying to achieve here? It's strange to me."
In comparison, he referred to Jadon Sancho's previous falling out with ex-Manchester United head coach Erik ten Hag.
Sancho is now thriving on loan at Chelsea, while Ten Hag was sacked earlier this season.
Cole said: "The Sancho situation could've been handled a lot differently. Now he's playing for Chelsea and scoring goals. Man United will look at that and say, 'We would've liked Sancho to be on form like that'.
"But because Ten Hag made it uncomfortable for him to be there, he had to find a new home where he can establish himself and be the player we know he can be."
Pressure continues to mount on Postecoglou amid a dreadful run of results, mitigated by a desperate injury crisis.
His first season in the Premier League was one of promise with a fifth-place finish, but they now sit eleventh.