Spurs manager Postecoglou faced a challenging atmosphere when he was booed and heckled by disappointed supporters at the Vitality Stadium. His team's lackluster performance resulted in defeat after Dean Huijsen scored a header in the 17th minute.
The Australian refused to go into detail about the heated exchange but said he understood the supporters' emotional reaction.
"I didn't like what was being said because I'm a human being but you've got to cop it," said Postecoglou, whose team have won only one of their last six games in all competitions.
"I've been around long enough to know that when things don't go well you've got to understand the frustration and the disappointment.
Trending"They're rightly disappointed tonight because we've let a game of football get away from us. I'm OK with all that.
"They're disappointed and rightly so. They gave me some direct feedback, which I guess is taken onboard.
"All I can say is, I'm really disappointed with tonight and I'm determined to get it right and I will keep fighting until we do."
Asked what was said by the travelling support, Postecoglou replied: "Probably not for here, mate."
Tottenham began brightly in Dorset but created little during the 90 minutes and were fortunate not to lose by a bigger margin.
Bournemouth midfielder Ryan Christie struck a post and the impressive hosts failed to capitalise on a host of other chances to put the result beyond doubt.
Spurs dropped below the Cherries, into 10th position, ahead of their London derby at home to high-flying Chelsea, live on Super Sunday, following the latest setback in a patchy season so far.
To compound a miserable evening for the injury-hit north London club, defender Ben Davies limped out of his 300th Premier League appearance and faces a spell on the sidelines.
"It looks like he's done his hamstring," said Postecoglou.
"Him and Radu (Dragusin) have played every game, it's the one sort of position we can't rotate.
"He'll obviously be out for a period of time now, we'll just have to wait and see how long it is.
"It's kind of the consequence of us having the squad we have at the moment."