Matthew Stott had to be restrained by City's Shrewsbury-born goal keeper Joe Hart and was arrested following Robin van Persie's late winner at the Etihad Stadium.
He was subsequently charged with pitch encroachment.
Speaking through his solicitors Stephen Lickrish and Associates he confessed his guilt – and said sorry to the Manchester United defender.
In a statement, the landscape gardener, from Knutsford, 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 also apologise to Manchester United and their fans."
The 21-year-old added: "I would like to thank Joe Hart for his actions when I came on the pitch." Ferdinand took to Twitter to thank Hart following the incident.
He then wrote:
Greater Manchester Police today charged nine people, including Stott, following the trouble which flared at the end of the derby.
Ferdinand was struck by a coin thrown from the crowd as he celebrated the late winner.
The person who threw the coin has yet to be identified.