Referee Lee Mason sent off City midfielder Fernandinho in the game and despite Sagna amending the post to remove the "10 against 12" part, he could not escape an FA charge.
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The FA alleges Sagna's post "questioned the integrity of the match official and/or alleged and/or implied bias on the part of the match official, and/or brought the game into disrepute".
Fernandinho was dismissed in the 32nd minute for a two-footed challenge on Burnley winger Johann Berg Gudmundsson.
City had an appeal against the decision rejected, leaving the Brazil international to serve a four-match suspension following his third red card of the season.
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