Ferdinand had blood pouring from a cut above his eye after being hit by a coin following Robin van Persie's late derby winner at the Etihad Stadium, and the United defender then had to deal with Stott coming on to the pitch towards him.
Stott had to be restrained by City keeper Joe Hart and was arrested and subsequently charged by police.
In a statement released by his solicitors Stott, a landscape gardener from Knutsford, Cheshire, said: "I would like to apologise to all those affected by my actions yesterday, particularly Mr Ferdinand and the other players.
"I am extremely ashamed of my actions. I have let myself down, my family down, my fellow fans down and Manchester City Football Club.
"I intend to write personally to Mr Ferdinand to express my extreme regret and apologies and also apologise to Manchester United and their fans.
"I would like to thank Joe Hart for his actions when I came on the pitch.
"I have been a fan of Manchester City all my life and I have been a season ticket holder for three years and I attend the games with my father. I have had the same seat in the section next to the away fans for those three years."
Stott is now facing a possible banning order but his solicitor said he had not been in trouble before and was not the "stereotypical drunken football fan".
Police have also charged eight other people for offences including racially aggravated public order, pitch encroachment and breaches of football banning orders.
FA chairman David Bernstein labelled the incidents "deplorable".
He said: "To see Rio Ferdinand with blood on his face is absolutely terrible. I think it's disturbing that we're seeing a recurrence of these types of incidents.
"We've had racial abuse issues, the odd pitch incursion, things being thrown at players - it's very unacceptable and has to be dealt with severely... in the strongest way we can.
"To my mind it's for the FA, the whole game of football and the authorities to work together to deal with this most severe matter."