Tottenham's interim boss received a red card in the second half of the club's 2-1 win, where he clashed three times with counterpart Roberto De Zerbi.
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In what was a fiery encounter in north London, Spurs edged out a narrow victory to boost their top four hopes in a game marred by controversy.
The Seagulls had two goals ruled out by VAR, with their second disallowed strike infuriating De Zerbi - resulting in both benches exchanging heated words.
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It led to Stellini and De Zerbi being sent off, with Harry Kane firing home a late winner for the hosts.
Speaking exclusively to talkSPORT's Ian Danter about his red card following his bust-up with De Zerbi, Stellini said: "I was not confused about being sent off.
"Because the rules say that I have to manage the bench, sometimes you can control the bench, sometimes you cannot, that was that moment.
"Maybe I have to do something to push back my staff, but in that moment, we felt aggressiveness from the other bench, someone reacted, which was not good.
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"I prefer to stay calm and be focussed, and use my energy to be focussed on the game and push my team to play at the best and to try to win.
"But what happened on the pitch, stays on the pitch, we don't have to speak about this, we have to be happy for the win."
Clarifying he was sent off for failing to control his coaching staff, he stated: "This is the rule. You have to manage the bench.
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"It's my job to do it, if you don't do it, probably the referee thought I have to do something different."
Commenting on De Zerbi wagging his finger in his face prior to the kick-off, Stellini remarked: "It was nothing in particular.
"I want to give respect to all the managers in the Premier League, because this is only the second game that I am the manager at the moment.
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"So what I can say to the other managers is only to be pleased to have this possibility, so it is not my job to speak about the other."
In his own interview with talkSPORT, De Zerbi said of his red card: "I'm usually respectful to everyone, and I want the same from other people to me."
He added: "During the game I never put any pressure on the referee, and when I saw the other bench put pressure eon the referee, I didn't like it, because it is not right.
"We have to be a coach on the bench, and nothing more."
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The result has seen Spurs maintain their hopes of finishing in the top four, as they sit just three points behind fourth-placed Manchester United.