A club spokesperson has confirmed they "are appealing the severity of the sanction" following Hutton's dismissal.
The Tottenham defender, on-loan on Wearside, was embroiled in an altercation with City striker Jozy Altidore at the end of the first half that resulted in referee Lee Probert dismissing both players.
Following a challenge between the duo, Hutton sparked the incident by throwing the ball at Altidore, who responded by headbutting the Scot, causing facial injuries.
Hutton is now poised to miss the final two games of this season at home to Manchester United and at Wolves, as well as the first match of next season.
Sunderland, though, are to make representations to the Football Association in the hope of seeing Hutton's punishment reduced.
Believing the suspensions are disproportionate, manager Steve Bruce said: "The two incidents don't warrant each other.
"He (Hutton) has thrown the ball at his back. It's not going to hurt Altidore, he is built like a horse. He might be angry, but to go and headbutt someone.
"That was below the belt and Alan is lucky not to be in hospital as he has a cut eye, bust nose and chipped tooth.
"The letter of the law says if you throw a ball at someone it is a red card, it seems strange, but it's the letter of the law."