The Togo international fired Spurs into an early lead at the Emirates Stadium, before being shown a straight red card for a reckless challenge on Santi Cazorla after just 18 minutes.
"I can't change who I am, or how I play the game, Adebayor told The Sun. "I will always go for it, I will never hide or be too afraid to get stuck in.
"Looking back, with the benefit of hindsight, yes it was rash. But equally, nobody can accuse me of ducking out, or not wanting to give it my all to try to help Tottenham.
"I will reflect long and hard on what I could have done differently because in the end my enthusiasm went too far. I have to accept responsibility for that. But my game is about passion and heart and I will never stop giving everything."
Prior to the weekend, Adebayor had not been sent off since February 2010, when he was dismissed for lashing out at Stoke City's Ryan Shawcross in an FA Cup tie while playing for Manchester City.