Postecoglou cupped his ear and looked at the Spurs away support after Pape Matar Sarr struck an equaliser, which was ruled out by VAR.
Chelsea eventually won 1-0, with Enzo Fernandez scoring on 50 minutes.
He remarked afterwards: "Yeah, tough game, always is when you come here obviously. It was tight, we had to fight hard to stay in it, which I think we did fairly well. Obviously Vic pulled off a big save, we had to defend pretty strongly at times. Always a threat going the other way, maybe should have been a little bit more clinical in that front third. But I thought we were in the game.
"Then conceded a really poor goal, which we've been doing too often, that's costing us. And that's really disappointing. But I thought our response from that was really good, positive. We did equalise and then that got ruled out, and then we had a couple of big chances towards the end. So yeah, really disappointed to not get something out of the game."
On cupping his ear, Postecoglou rejected claims he was angrily reacting to the away support.
"Jesus mate, it's incredible how things get interpreted. We'd just scored, I just wanted to hear them cheer. Because we'd been through a tough time, and I thought it was a cracking goal. I wanted them to get really excited. I felt at that point we could potentially go on and win the game. I just felt momentum was on our (side).
"It doesn't bother me, it's not the first time they've booed my substitutions or my decisions, that's fine, they're allowed to do that. But we'd just scored a goal, just scored an equaliser, I was just hoping we could get some excitement. If people want to read into that that somehow I'm trying to make a point about something, like I said, we'd been through a tough time, but I just felt there was a bit of a momentum shift there. If they get really behind the lads, I thought we had the momentum to finish on top of them."
Asked if he had concerns of causing a rift with the fans, the Spurs manager also said: "You know what, I am at such a disconnect with the world these days, that who knows, maybe you're right. I don't know. But that's not what my intention was."
On the away Spurs barracking him in the second-half, Postecoglou was dismissived.
He added: "It just doesn’t affect me. If that’s what the fans feel and if they feel I’m not doing a good job then they’ve got every right to express it. They pay their hard earned, they follow the club and they’ll be here long after I’m gone. It doesn’t affect me.
"What I focus on are the things I can control. I can’t control fans, I can't control but many things but I can control our football, the way we play and the way we conduct ourselves and that’s what I concentrate on."