Sagna posted a picture of Manchester City celebrating a goal on Instagram following their 2-1 victory over Burnley, which was accompanied with the caption "10 vs 12".
The caption was in reference to referee Lee mason, who had sent off Manchester City midfielder Fernandinho in the victory.
FA rules state that players and managers may criticise referees' performances, as long as their integrity isn't questioned, something which Sagna failed to do.
The Frenchman was therefore handed a £40,000 fine for the post, but the club are thought to be unhappy with the punishment.
Sagna accepted the misconduct charge and deleted the post from his Instagram account and it is thought that City will appeal the punishment given to their player, as they deem it excessive.