The Australian coach was jeered by supporters as Spurs lost 1-0 to Bournemouth in the Premier League on Thursday (05.12.24) but says it is more important that fans back the team rather than the manager.
Postecoglou said: "They aren't behind me, they are behind the club. I have got no interest in who is behind me.
"Last night you have to figure the fans who travel to Bournemouth are fairly hardcore supporters.
"They weren't happy with what they saw and they felt like they needed to give some feedback. I took the feedback onboard and we move on."
Spurs have only won one of their last six matches in all competitions but Postecoglou but has vowed to "fight" to bring success to the club.
He said: "As I said last night, no messages. I am here, I am going to fight to make sure we bring success to this football club.
"Nothing really changes. Where there is doubt, whether that is internally or externally, it just gets my resolve stronger to make sure we get it right."
Spurs have been hit hard by injuries in recent weeks but Postecoglou is refusing to use it as an excuse for his side's inconsistent performances.
He said: "For me the disappointment last night, there was a repeat of cycle of us going into games, starting well enough but then allowing the opposition to get a grip on it by either conceding a sloppy goal - like we did last night - or not taking our opportunities.
"We need to break that cycle, irrespective of where we are at at the moment. We know we are really thin on the ground in terms of squad numbers. We know there is not a lot of opportunity to rotate and rest players. We paid the price with Benny [Davies] last night.
"Those are known things. What also is known is we repeatedly shot ourselves in the foot in games like last night and we need to change that."