He was angered by the decision to award the penalty against Andreas Weimann that led to City going 2-0 ahead.
Lambert will have to watch from the stands when his side take on Arsenal at Villa Park on Saturday.
The FA charge related to "language and/or behaviour amounting to improper conduct".
After the game, Lambert said: "I haven't a clue what [assistant referee Adrian Holmes] saw. We were well in the game - we had a foothold in it, and that is a big thing coming here but the penalty was a really shocking decision."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.