The Sky Blues’ captain was sent off by referee Mike Dean for an adjudged two-footed challenge on Jack Wilshere after 73 minutes.
This could result in a three-match ban for the Belgian, which may be increased by the FA.
However, when asked by Sky Sports whether he will appeal the decision, Mancini replied:
“Yes. This is absolutely not a red card. He has one foot taking the ball, the other is back. I think the referee made a mistake.”
Kompany’s dismissal was not the first of the game, with Arsenal’s Laurent Koscielny’s receiving a red card for hauling down Edin Dzeko in the first-half.
The Bosnian missed the resulting spot-kick, but atoned for his error with a close range tap in after James Milner had opened the scoring.
Mancini was happy with the three points, but was left frustrated by a lack of killer instinct from his attacking players:
“It was easier after the (Koscielny) sending-off, but in the second half we were too soft and missed three or four goals.
“We could have done better with our strikers when we attacked in the second half because we needed to close the game.”
The result keeps City seven points behind local rival United at the top of the table, and Mancini believes that the title is far from being decided:
“We know United are strong, but the season is long and we need to work.”