The defender was shown a red card on the advice of a linesman following a last-ditch tackle on visiting striker Edin Dzeko.
Referee Andre Marriner looked to be pointing for a corner after Rose diverted the ball behind Hugo Lorris' goal but after consultation with his assistant, awarded a penalty.
Yaya Toure sent the Frenchman the wrong way to put City 2-0 ahead in the 55th minute and within three minutes Dzeko had put the game beyond the home side.
Etienne Capoue gave Spurs brief hope shortly before the hour mark but further goals from substitute Stevan Jovetic and Vincent Kompany completed the rout for City.
After the match, Tottenham boss Tim Sherwood gave a strong hint he would appeal against the card and subsequent three-match ban which would rule Rose out of games against Hull, Everton and Newcastle.
"I think Andre got it right in the first place when he called it as a corner," he said. "But, unfortunately for us, the linesman decided that Andre got it wrong.
"I think Danny's making a last-ditch tackle so he's having to lunge in there a bit. He clearly wins the ball. I think we will appeal."
However, City boss Manuel Pellegrini disagreed with Sherwood's views claiming assistant Scott Ledger was correct to flag for the infringement.
"It was a clear penalty and a clear red card because he was the last man," he said. "The sending-off was not the thing that changed the game. The game was over and completed from the beginning for our team."