Mostert was sent off after 11 minutes for a tackle on Italy fly-half Paolo Garbisi which the match officials said at the time was illegal.
The appeal committee disagreed, however, suggesting the initial contact was on the shoulder and any head contact negligible.
It was the second red card in as many weeks for the Springboks after lock Lood de Jager was sent off in their 32-17 victory over France, much to the displeasure of their coaching team.
"As a team, we’re doing everything we can to play the game in the right spirit," assistant coach Mzwandile Stick told reporters in Dublin.
"But are we treated fairly? At the moment, I don’t think so."
Lock Harry Hockings received a 20-minute red card on debut for Japan against Wales in Cardiff on Saturday, but has also had that rescinded by an independent appeal committee.