The £50m summer signing from Tottenham Hotspur was given his marching orders just before the half-time whistle after receiving two yellow cards from referee Bobby Madley inside three minutes.
"Gutted with last night," the right-back posted on his Twitter page on Tuesday evening.
"I apologise to the fans and my teammates. They did amazingly well to get back into the game and get a point #MCFC."
Walker will miss Man City's trip to Bournemouth on Saturday as a result of his dismissal.