Ange Postecoglou was involved in an incident with a Tottenham supporter who allegedly kept insisting his side should throw the game against Manchester City and deny Arsenal the chance to win the title.
On Tuesday Spurs needed to beat City at the Tottenham Hotspur Stadium to keep hopes of a top-four finish alive.
In doing so, however, they would have handed North London rivals Arsenal the advantage in the Premier League title race.
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Postecoglou's men ultimately fell to a costly 2-0 defeat, in what was a noticeably flat atmosphere.
The Australian was bewildered before the game by the suggestion that some Spurs fans would be happy to lose to City if it damaged Arsenal’s title chances.
And in one incident, Postecoglou was captured on video arguing with a Spurs fan in the stadium.
The 58-year-old turned to a fan behind the dugout and appeared to shout: “What did you say, what did you say before that? I wanted to know who you are.” Fans on social media have claimed the supporter kept urging Tottenham to throw the game.
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Elsewhere, Erling Haaland's 51st-minute opener was met with home supporters chanting: "Are you watching Arsenal?"
After the game, when asked if the peculiar atmosphere influenced his players, Postecoglou said via BBC: "Of course it does. It is what it is. I can't dictate what people do.
"They're allowed to express themselves any way they want. But yeah, when we've got late winners in games it's because the crowd's helped us."
He added: "The foundations are really fragile. The last 48 hours have shown me that.
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"It's inside the club, outside the club. Outside, inside, everywhere. It's been an interesting exercise. It's just my observations, mate."
When quizzed on the Spurs fans' chants, Postecoglou replied: "I'm not interested, mate. I just don't care. Maybe I'm out of step, but I just don't care, I just want to win.
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"I want to be successful at this football club, it's why I was brought in. So what other people, how they want to feel, and what their priorities are, are of zero interest to me.
"I know what's important to build a winning team - that's what I need to concentrate on."
Chris Byfield