Brian Little said that Williams' sending off ended City's chances of getting back into the game, and has now fined him the maximum two-weeks' wages.
Little said after the game: "In all fairness it was a bad decision not to award us a free-kick in the first place but for our player to react what seemed like some four or five minutes later is pretty unforgiveable.
"We didn't need that. We'd just made substitutions, we were under pressure and not playing well. Effectively that finished the night for us."
As well as receiving disciplinary action from the club, Williams will be suspended by the league for up to three games. He will definitely miss the local derby with Scunthorpe, and possibly the trips to Oxford and Leyton Orient.