The Australian saw his charges score first in each half, but then become overwhelmed as the Hammers switched on, scoring three goals in each half to silence the Glasgow support.
What a performance from the lads 😍— West Ham United (@WestHam) July 24, 2021
🎥 All of the action from today's 6-2 win at Celtic Park! pic.twitter.com/x3FfhfVsuo
Callum McGregor scored Celtic's first shot inside the first 10 minutes, pouncing on a poor throw-in before firing home from outside the box.
While Postecoglou's men continued to push for a second, things came apart when Michail Antonio was allowed to score twice and win a penalty that Mark Noble converted to make it 3-1 at the break.
Celtic again started strongly in the second half when Ryan Christie slotted home on 51 minutes, but it was Said Benrahma that replied for West Ham just three minutes later before Jarrod Bowen and Armstrong Okoflex put the seal on the win for the Londoners.
“I think there were some positives but there are certainly some areas that were very disappointing," Postecoglou said after the game.
"We didn’t really take the opportunity to test ourselves against a quality opponent.
"We started brightly enough, we started very well and created some good chances.
“We scored the goal and then we just seemed to make a mistake. Mistakes are going to happen but again the reaction to it wasn’t great.”
Celtic now heads to Denmark with the game against FC Midtjylland locked at 1-1, and Postecoglou knows he needs a positive reaction from his team in order to progress in Europe's elite club competition.
“We have three or four days and it’s as much about the players as it is about us," he said. "My job is to continually work with them along with the staff to give them the tools they need.
“It’s about them as well, it’s about them growing and understanding what you can and can’t do out on the football field – and what approach you need to take.
"It’ll be as much about their response as it is about me giving them guidance moving forward.”