The Togolese striker opened the scoring after 10 minutes, but was shown the red card following a reckless tackle on Santi Cazorla, with the Gunners going on to make full use of their one-man advantage.
Despite the loss, the Portuguese manager refused to lay the blame at the striker's feet and when asked by Sky Sports News whether the game swung on Adebayor's red card, he said: "No - first I am very, very proud of my players, I think it was too much time playing with 10 men.
"The sending off, these things happen in football. I think the referee made the right decision, but today I'm very proud of my team."
The 35-year-old chose to focus on other areas where he felt the game was lost - losing the third goal just before half-time, and Gareth Bale wasting a great opportunity to set up Jermain Defoe to reduce the deficit at 4-2.
He continued: "There are two key moments in the game; the 3-1 left us with a big margin to come back, but there were also a couple of chances for the 4-3.
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"Had we taken the game to a one-goal difference in the second half I think we could have gone all the way through because we certainly had the football, the passion, the ambition and the desire with 10 men, so I don't take it as a defeat.
"I take the result but I am extremely proud of the team."
The White Hart Lane boss revealed he will not punish Adebayor for his early red card, adding: "Players go to dispute the ball not with the intention to do any harm but sometimes situations like this happen."
The manager also suggested the nature of the crowd left him believing a shock comeback was on the cards, and disputed Arsenal's superiority in the game as purely being down to their numerical advantage.
"We wanted to go to 3-2 and the players really felt it, and really believed if they scored and brought the result to a one-goal margin [they could come back]. The stadium was very very unbalanced," he added.
"It's easy to do 20 passes and score a goal against a team with 10 men and look all brilliant, but I don't think we were so poor. I think we were very, very good and we certainly showed it between 11 and 10 men."