Spurs suffered a 1-0 defeat to the Cherries on Thursday night, with teenager Dean Huijsen bagging what went on to be the winner early in the first half.
The away end let their feelings known at the final whistle, with a number booing their side off the pitch.
Postecoglou, who came over to show his gratitude to the supporters, was also booed.
He was seen approaching the away end, with the Australian expressing himself with his hands as he reacted to the criticism.
Two stewards stood in the way of him and the crowd, with one extending their arm out.
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Footage shows Djed Spence putting his arm on Postecoglou's back as he turned away and towards the tunnel.
Asked about the reception from the fans and the booing, he told talkSPORT: "Yeah, well rightly so.
"They're disappointed and I got some pretty direct feedback, which is always healthy mate."
In his post-match press conference, he continued: "I didn't like what was being said because I'm a human being but you've for to cop it.
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"I've been around long enough to know when things don't go well you've got to understand the frustration and disappointment. And they're rightly disappointed because we let a game of football get away from us. But that's OK. I'm OK with all that.
"All I can say is I'm really disappointed and I'm determined to get it right and will keep fighting until we do."
Bournemouth had the better chances on the night, with Spurs, in truth, lucky to escape with conceding just one goal.
The Cherries managed 21 shots.
Addressing the number of chances his side gave up in the clash, Postecoglou said: "Yeah well that's because we were chasing the game.
"When you go a goal down, in the second half you're on the up and up and chase the game.
"That's going to give them space and that's what they want and what they're good at, so."
Bournemouth have jumped above Tottenham in the table after claiming all three points.
The Cherries sit in ninth, one point above tenth place Spurs.
And the north London side's 4-0 thumping of reigning Premier League champions Manchester City last month now feels like a distant memory.
talkSPORT's resident Spurs fan, Jamie O'Hara, said on the Sports Bar: "It's hard work you know, watching Spurs. One minute you're up, then you're down, then you're up, then you're down.
"And you know what? It's just, it's painful. We are painful to watch. Painful. Because you know there's a big performance in there because we've seen it.
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"Aston Villa. Man City. You go away from home, you get beat by Bournemouth.
"I know everyone loves Ange, you know, in terms of like the attacking football. I can't, I'm getting bored of watching this."
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