The Northern Ireland international was given his marching orders in only the 15th minute after tangling with Shaun Wright-Phillips as the duo chased a long ball over the top.
Referee Steve Tanner dismissed McCartney after consulting with his assistant and City went on to defeat the 10-man visitors courtesy of Micah Richards' second-half header.
Black Cats boss Ricky Sbragia was bemused by the decision and admitted after the match he was hoping Tanner would view the incident again, with the club now confirming that an official appeal has been lodged with the Football Association.
A statement on the club's official website read: "Sunderland have decided to appeal against the sending off of defender George McCartney in yesterday's Premier League game at Manchester City."
Sbragia insisted that Wright-Phillips would not have beaten goalkeeper Marton Fulop to the ball even without the minimal contact from McCartney.
The Black Cats boss said earlier: "He made some sort of contact, but I thought the keeper already had the ball in his hands. He was never going to get the ball.
"The ref ummed and aah'd and took the decision to send the player off.
"It changed the game and I hope he will look at it and rescind the red card."