City's captain was sent off towards the end of a 2-0 win after referee Mike Dean ruled he had tackled Jack Wilshere with two feet.
Kompany is facing a three-match suspension which could be increased if the Football Association decides any appeal is frivolous.
The Belgian took to Twitter to give his side of the story, accompanied by a photo which appeared to show one of his feet being on the floor as he made the tackle.
"No grudges against the referee, I understand the difficulty of the job," he wrote. "About the tackle: 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."
Asked whether City would fight the ban, manager Roberto Mancini told Sky Sports: "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 evened the numbers following Laurent Koscielny's early red for hauling down Edin Dzeko, and although the striker missed the resulting penalty he went on to add to James Milner's first-half goal.
The result kept City within seven points of leaders Manchester United, but the manager was frustrated by his forwards' failure to kill off the game long before the end.
He said: "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."