Despite the apology, FA chief executive Ian Watmore has insisted that the FA will "take a close look" at both controversial incidents from the match.
"I was pretty unimpressed really because the problems between the Arsenal fans and Adebayor are well documented, and he ran the whole length of the field to celebrate, so I think we're going to have a good close look at that one on Monday when we see it properly in the cold light of day," Watmore told The Press Association.
"I thought the stewards did a great job of calming the situation down and it was to Manchester City's credit nothing worse happened.
"Our governance team will take a good look at both of the incidents that have been highlighted and will come to the media with the answers early next week."
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The secretary of Arsenal's north-west supporters' club, Terry Milner, has called on the FA to hand a hefty punishment down to the Manchester City striker Emmanuel Adebayor for his actions in Saturday's win over the Gunners.
The Togo international looks to have landed himself in hot water for an alleged stamp on Robin van Persie and for his extravagant goal celebration, incidents which the FA have confirmed they will now investigate.
Milner, however, is in no doubt that the striker deserves to be punished and is clearly expecting a hefty penalty.
"I hope they don't put the two incidents together and effectively let him off with one," he told the Manchester Evening News.
"What he did to Van Persie was assault and that alone probably deserves a five-match ban. Then there's the fans incident. I think Gary Neville was charged for something similar against Liverpool a few years back so there's that too."
Milner also insisted he believed the striker’s goal celebrations were pre-meditated and insisted there was no excuse for his behaviour.
"My feelings towards this is that it proves how little class he has about him. It was pre-planned, there was no way that was off the cuff," he added.
"I understand that some fans have booed and jeered him and I saw things being thrown on the pitch, plastic chairs and stuff, which was wrong. But what the hell was he doing?
"He is earning, reportedly, £180,000 a week and he should be able to rise above booing and name calling.
"If you gave me £180,000 a week you could call me anything you wanted."