Nine charged over derby crowd trouble
United defender Ferdinand was cut just above his left eye after being hit by the coin while celebrating Robin van Persie's late goal which gave the Premier League leaders a 3-2 win at City's Etihad stadium.
"Despite fierce rivalry and high tension there was no major disorder," Greater Manchester Police chief inspector Steve Howard said in a statement.
"However, we will continue to investigate the coin throwing incident and are determined to work with the club to bring the perpetrator to justice."
City fan Matthew Stott, 21, ran on to the pitch and tried to reach Ferdinand as he was recovering but was restrained by the home side's goalkeeper Joe Hart.
Stott, one of two men charged with pitch encroachment, issued an apology through his solicitors on Monday, saying: "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."
A total of 13 arrests were made by police. Of the nine people charged, one was for a racially aggravated public order offence.
Those charged are due to appear at Manchester City Magistrates' Court on January 4.
Manchester City also issued an apology to Ferdinand "unreservedly condemning the actions which led to him being injured" and in a strongly worded statement said they would discipline any fans found guilty of offences.
The FA is also investigating the incident which led to calls from the governing body's chairman David Bernstein to ban those found guilty of anti-social behaviour at football matches for life.
Professional Footballers' Association boss Gordon Taylor has suggested netting should be erected in vulnerable stadium zones, including corner flag areas, to protect players from objects thrown by the crowd.