Werner was hooked at half time following a disappointing 45 minutes where Spurs struggled to get a foothold in the game, despite still being on level terms at the interval.
Postecoglou then saw his side concede two minutes into the second half courtesy of Hamza Igamane, but it was Werner's replacement Dejan Kulusevski who netted the equaliser to spare Spurs' blushes.
The result means Spurs are now winless in five games since their remarkable 4-0 win away to Manchester City, further raising the pressure on the Australian manager.
Spurs have won just one of their last eight games, causing a slide in both the Premier League table, where they are now in the bottom half, and in the 36-team standings in the Europa League.
Postecoglou singles out Werner for poor performance in Rangers draw
Speaking to the media in his post-match press conference, Postecoglou was quizzed on his decision to substitute Werner at half time, explaining it was a tactical decision.
Visibly unimpressed, Postecoglou quickly answered: "He wasn't playing anywhere near the level he should.
"When you've got 18-year-olds [playing], 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. His performance in the first half wasn't acceptable."
Postecoglou's comments are not only surprising due to the outing of one individual player, but also because he claimed he is not one to dig players out in public as recently as Wednesday.
When talking about recent comments made by Cristian Romero where he criticised the Spurs board, Postecoglou stated it may have not been the right thing to say publicly, before making a contradictory comment.
"Cristian realises that a lot of what he said was good, but some was not the right way of dealing with it, the same way I would not criticise a player publicly." Postecoglou claimed.
Sherwood-esque outburst from a frustrated Postecoglou
Managers coming out publicly and criticising players individually is a rare occurrence, especially in the Premier League.
However, harking back to 2014 when Tim Sherwood was in charge at Spurs, a similar scenario happened.
Following a 4-0 defeat at Stamford Bridge to London rivals Chelsea, Sherwood publicly criticised his entire team following the humbling result.
Sherwood told Sky Sports in his post-match interview that there were players in the squad he could not count on, and that there was a lack of characters in the team.
The former Spurs player left his role as manager at the end of the season just a few months later, and the same fate could beset Postecoglou unless upcoming results improve.
Written by
Andrew Delaney