Ferdinand was seen wiping blood from his face following the incident which took place in the aftermath of United's injury-time winner in their 3-2 victory at the Etihad Stadium.
City trailed 2-0 but fought back to equalise before Robin van Persie's late free-kick secured three points for United.
Praising the football, United manager Sir Alex Ferguson told Sky Sports: "It's just unfortunate towards the end a City fan runs on and then they throw coins at our players and that. I don't think you need that.
"The same thing happened at Chelsea which was masked really by all the other things that happened.
"But, you know, two fantastic teams today [Sunday], I think, and a fantastic game of football, and it could do without that."
Van Persie was unaware Ferdinand had been injured when he was questioned immediately after the game.
The Dutchman said: "I missed the thing with Rio so I will have to look back at it, but that should not really happen on a football pitch."
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The violent scenes were in contrast to earlier in the match.
According to Greater Manchester Police's (GMP) Twitter feed, there had only been one arrest by 2pm of a suspected ticket tout outside the stadium.
However, during the game GMP announced that another man was arrested inside the ground on suspicion of committing a racially aggravated public order offence after officers heard racist chanting.
Earlier, the match commander Supt Craig Thompson said: "I have every confidence this match will mirror the two derbies last season and the football will be the only talking point."
After Ferdinand was struck by the missile, a Manchester City fan ran on to the pitch in the England defender's direction.
He slipped and fell to the ground as he approached the player up to 10 yards away and was then obstructed by City keeper Joe Hart who pushed him away.
The supporter was then led away from the pitch.
The incident was not shown to viewers of the match on Sky Sports.
When Ferdinand left the pitch at the end of the match he was seen to have an object in his hand which he showed to referee Martin Atkinson before he threw it to the ground.
A message on Ferdinand's official Twitter account posted at 4.34pm read: "what a result,3points! Sweet! Whoever threw that coin,what a shot! Can't believe it was a copper 2p....could have at least been a £1 coin!"
Another Ferdinand tweet added: "Respect to Joe Hart for protecting that idiot who ran on!! Love the banter between fans but there is a point when it goes too far...calm it!"