The England international had been warned by United's disciplinary advisers that he could be hit with a four-match ban, rather than the mandatory three-game suspension, by the FA if they deem his appeal to be 'frivilous.'
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But United manager Ferguson insists he is backing Ferdinand's appeal and insists he can overturn the charge and be free to face Arsenal at the Emirates on Sunday.
Ferguson said: "If it's a fair hearing then he (Ferdinand) has a good chance. He was wrestled and punched, all sorts of things happened to him, and he was just trying to wrestle free from it.
'Unfortunately for us, he's caught him [Fagan] on the back of the head. But we will contest it."
United clinched a 4-3 aggregate victory over their Mancunian neighbours with Wayne Rooney's winning goal, two minutes into stoppage time.
But despite his central role in United's win, Rooney insisted that much of the credit for the victory is due to midfielder Darren Fletcher, who produced a memorable performance for the home side.
Rooney said: 'Fletch has been playing ike this for years now and he underlines what United are all about.
'He works hard and has a great attitude, but he has only been getting the credit for the last couple of years.
'He rises to the big occasion, but he is a world class player and I wouldn't swap him for any player in the world.
'We were deserved winners. We started well and when we went at City, they didn't know what to do.
'We had players like Fletch, Michael Carrick and Paul Scholes ratting about and thankfully we scored at the end.'