Arsene Wenger's young Gunners were on the receiving end of a 5-1 drubbing at the hands of their arch-rivals, which saw an angry confrontation between the two Arsenal strikers towards the end of the match.
The incident is now being investigated by the Football Association, who have requested relevant television footage after referee Howard Webb confirmed he did not witness the whole event.
Adebayor - who was handed a four-match ban after being sent off just minutes after coming on in last season's Carling Cup final defeat to Chelsea - accepts tempers were allowed to boil over in the heated atmosphere, and offered an unreserved apology for his actions.
"I am sorry for the disagreement with my team-mate Nicklas," Adebayor said on the club's official website. "We are both passionate about this club and sometimes that can be projected in the wrong way.
"It was a mistake. We want to focus on the games ahead and rely on our squad's great togetherness to achieve a fantastic season."
Adebayor - who was handed a four-match ban after being sent off just minutes after coming on in last season's Carling Cup final defeat to Chelsea - accepts tempers were allowed to boil over in the heated atmosphere, and offered an unreserved apology for his actions.
"I think that we should have been more calm during the game and although I was pleased to get a goal back for the team when I came on, I am sorry for the disagreement with my team-mate Nicklas," Adebayor said on the club's official website.
"We are both passionate about this club and sometimes that can be projected in the wrong way.
"It was a mistake. We want to focus on the games ahead and rely on our squad's great togetherness to achieve a fantastic season."
The Adebayor, 23, has been in fine form for the Gunners, with his goal on Tuesday night when coming off the bench a 16th of the campaign.
Adebayor firmly believes the events at White Hart Lane will not unsettle Arsene Wenger's squad, which remains very much in the hunt for honours.
The Togo striker said: "We are a strong unit and what happened last night against Spurs will strengthen our desire and determination to compete for other targets."
Skipper Gallas has called for "upset" Arsenal to unite from their disappointment - and knock revitalised Newcastle out of the FA Cup this weekend.
Wenger reflected afterwards the defeat was all part of the "learning process" and maintained he had "no regrets" about selection policy in a competition which is clearly not the Gunners' main priority.
However, the likes of skipper Gallas, Cesc Fabregas, Alex Hleb, Gilberto and Adebayor, all featured at some stage - but their experience could not, on this occasion, help bring the best out of the likes of Justin Hoyte, Abou Diaby, Bendtner and a particularly disappointing Theo Walcott.
Gallas, though, insists now is the time to look forwards and not reflect on what might have been as the Gunners saw their near nine-year unbeaten run against Spurs come to an abrupt end.
"All the young boys wanted to go to Wembley and I know it is difficult to accept," said the French defender.
"The fans are upset and we are upset. All the club are upset - and we have to accept it.
"Now we have to be strong and forget everything because on Saturday we have another big game which will not be easy."
