The Hoops desire to go all the way to the final whistle has been a feature of the Parkhead club under the Australian boss and they were asked questions again against their bitter rivals in a thrilling Old Firm encounter.
The visitors had started well with Japan striker Daizen Maeda scoring in the fifth minute after taking advantage of poor Gers defending.
The Light Blues responded and Ryan Kent curled in the equaliser two minutes after the break before skipper James Tavernier slammed in a penalty to make it 2-1.
However, three minutes from the end of normal time, Maeda's compatriot Kyogo Furuhashi levelled to keep Celtic nine points clear of their Glasgow rivals at the top of the table.
Postecoglou said: "It's the way this group is, the way we have created the environment.
"There isn't anything like a lost cause. You go till the final whistle and nothing changes. You have to do that.
"For that to be effective, you have to do it on a weekly basis. And we do.
"Even in our comfortable victories, you'll still see us being really aggressive till the last minute.
"The players are conditioned to think that way and play that way. It's easy for me to talk about it, but in today's environment, and the way the game was, it would have been almost natural to say 'jeez, it's not going to be our day'. But this group of players just doesn't do that.
"It was a cracking game of football, a good derby. Both teams were going at it.
"We started the game really well and then just lost our way a little bit, the last 10-15 minutes of the first half we were giving the ball away unnecessarily, uncharacteristically for us, without a great deal of pressure.
"That allowed them to get that little bit of belief and obviously they came out at the start of the second half really strong.
"We struggled to get to grips with the game but again when it was required the players found the will and character to get the goal to get us a result."
Postecoglou revealed why Greece striker Giorgios Giakoumakis came on as a second-half substitute to complement Furuhashi rather than replace him.
The Celtic boss said: "We needed goals. Kyogo's pretty clever. He can drop in as a 10, he has played that in his career.
"So I just felt at that time that we needed a goal. Rangers started to retreat a bit which meant that hopefully we would get more balls in the box.
"And if we did that, having extra bodies in there would help us. It worked out that way."
Canada international right-back Alistair Johnston was thrown in for his Celtic debut and Postecoglou was impressed by the 24-year-old's performance.
He said: "I thought he was good. It's a difficult game to throw him into. Not only is it a derby, it's away from home and also we all knew it was a big game for a number of reasons.
"For the most part, he handled himself really well. He was solid defensively. He was up against a very good player in Ryan Kent.
"For the most part, I thought he handled it really well, but there is more to come from him, especially in an attacking sense once he gets to understand our games. He won't get a sterner test than that as a Celtic player. He came through it really well."