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Sagna, 32, posted a photo with the caption "10 against 12.. but still fighting and winning as a team" on the social network following City's 2-1 victory against Burnley on January 2.
It was seen as a criticism of referee Lee Mason after City had been reduced to 10 men for an hour after Fernandinho was sent off for a lunge on Johann Berg Gudmundsson.
Sagna, who was later involved in an altercation with Burnley midfielder George Boyd which Clarets boss Sean Dyche felt should have resulted in a red card, appeared to take issue with decisions made by Mason in the Instagram post after the match.
Although fined by the FA, Sagna escaped a suspension and was warned over his future conduct. The player subsequently appealed against the sanction, which the FA confirmed on Thursday had been dismissed.
"Bacary Sagna's appeal against his 40,000 fine for breaching FA Rules on media comments has been unsuccessful," the FA said.
"The player, who was also warned as to his future conduct, contested the sanction set down by an Independent Regulatory Commission after it heard he admitted making a comment which 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.
"However, an Appeal Board dismissed this appeal and the original sanction remains in place."
