Referee Mike Dean showed the City captain a straight red for a forceful lunge on Arsenal midfielder Jack Wilshere.
Kompany was incensed at the decision at the time, claiming that he won the ball cleanly and fairly.
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Kompany tweeted: "No grudges against the referee, I understand the difficulty of the job. If the ball is overrun by the opponent and a 50/50 challenge occurs, collision is inevitable.
"Ultimately I'm a defender: Appeal may work or not. I will never pull out of a challenge, as much as I will never intend to injury a player."
Manchester City manager Roberto Mancini was also bemused at Dean’s decision to send off his central defender.
Speaking to Sky Sports after the game Mancini confirmed the club would appeal the red card.
"This is not a red card, absolutely not," Mancini fumed.
"He has one foot to take the ball, the other is left. I think that the referee made a mistake there.
"It was not a sending off for Vinnie because Vinnie took the ball with only one foot after anticipating the opponent."
If the ban is upheld Kompany will miss City’s next three fixtures against Fulham, QPR and the winners of the FA Cup replay between Stoke City and Crystal Palace.