City were reduced to 10 men in the 32nd minute of the match, when referee Lee Mason sent off midfielder Fernandinho.
The FA said the post, which was later deleted, "questioned the integrity of the match official".
The 33 year old has also been warned about his future conduct.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!