Adebayor was shown a straight red card after a tackle with Santi Cazorla in the 18th minute.
"I'm sad, I'm disappointed," Adebayor told the Spurs website.
"I scored my first goal of the season and I was so happy, but then it was a 50-50 ball, I went for it and the referee decided to give me a red card.
"It was difficult to let the team down like that.
"We had to play 70 minutes without me, with 10 players, and especially at Arsenal you know how difficult the game will be.
"Even with 10 men the team showed character. They tried to come back and it was a tough one. We have to take the positives out of the game, get our heads right and keep going."
He added: "I tackled for the ball, it was 50-50 and unfortunately, Cazorla touched the ball before me and there was contact between him and myself, that's for sure.
"That's football. We all have to learn from our mistakes and especially me, after scoring, I don't have to tackle. I don't know why I did that. I just wanted to help my team-mates, I wanted to win the ball back for them, but it went the wrong way."