The 25-year-old was dismissed by referee Chris Foy for a two-footed lunge on United winger Nani, however the punishment was deemed on the harsh side as the Belgian came away from the challenge with the ball.
However, City's failure to see the ban overturned, which is increased to four matches as the red card represents Kompany's second of the season, leaves Roberto Mancini without his influential skipper.
After the game at the Etihad Stadium, Mancini said: "There is no way Vincent shouldn't play against Liverpool in the Carling Cup semi-final on Wednesday. It was 300% not a sending off."
The defender will miss both legs of the club's Carling Cup semi-final against Liverpool, which sandwich the league clashes with Wigan Athletic and Tottenham Hotspur.
The loss is further compounded by Kolo and Yaya Toure's departure to the African Cup of Nations, which is likely to leave City without the Ivory Coast pair until mid-February.
With Mancini unlikely to bring in defensive back-up during the transfer window, Joleon Lescott and Stefan Savic will be trusted with guiding City through a vital period in the context of their season, with domestic cup and league success hinging on upcoming results.