Postecoglou was seen confronting away fans after defeat at Bournemouth on Thursday.
Ahead of Sunday's derby against Chelsea, the Australian 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."
Asked if he had a message for Spurs fans, Postecoglou 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."
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