Jota cancelled out Christopher Nkunku's first-half counter-attack goal two minutes after the interval but Celtic could not build on the goal.
The home side hit the post and had a second goal disallowed for offside following a VAR intervention before Joe Hart gifted Leipzig possession and promptly conceded the first of two goals from Andre Silva.
Celtic never recovered as the German side dominated to leave Celtic bottom of Group F with one point from three matches.
Postecoglou, who admitted that a knee injury that forced Callum McGregor off "doesn't look good", said: "For the most part we matched them, we were aggressive and created some good opportunities.
"We had some really good chances in the first half, were well in the game, scored a good goal to get level and just got a bit negative in our mindset after that, especially with the ball, and sort of invited pressure.
"You can't give away goals like that at this level and we paid the price. Momentum went their way after that."
Hart passed the ball straight to an opponent while looking to find Greg Taylor but Postecoglou felt the former England goalkeeper was put into too many difficult positions.
"It's not about the mistake," he said. "Before then we had a lot of the ball and we were just passing it back to him for no reason. You are doing what you think is safe but it's not really who we are.
"First half, we played the ball through the lines. Sometimes we would make a mistake but that's okay, you are making a mistake trying to be positive.
"I just felt that it was creeping in before that. After we scored and got level we almost wanted to settle for that and kept passing the ball back to him.
"A mistake's a mistake, it's not about that, it's about what's the lead-up to that mistake, what are we doing? Are we playing our football? Are we showing the same sort of endeavour we were before then?
"I could see it coming. If it wasn't Joe making the mistake it would have been someone else because when you get into survival mode, the best you will ever do is survive.
"When you come away from home in a game like this and have fought so hard to claw your way back into it, you don't want to survive, you want to actually stay in that positive mindset where you can hurt the opposition and make them uncomfortable."
There was also bad news for Leipzig with captain and goalkeeper Peter Gulacsi suffering a serious knee injury.
The Hungary international sustained an anterior cruciate ligament tear in his right knee and will be out for a lengthy period, the club said.