The Club say they are 'bitterly disappointed' they have not been given the right to appeal after Funso Ojo was sent off at the Dundee United game on Saturday November 20.
The Club say they believe the governing body "failed to show any flexibility, considering the options they had at their disposal to right this wrong".
Steven Gunn, Director of Football at AFC said: "As we understand it, the Referee and the SFA’s Head of Refereeing Operations, immediately after seeing replays of the footage, recognised that the Referee had been mistakenly advised by his assistant referee that it was Funso that had pushed a spectator rather than the other way around. As a result, Funso was given a second caution. Pushing a spectator is, in fact, a sending-off offence which would have given us a right of appeal.
"We don’t doubt that, had the Referee been aware of the correct facts, he would have taken every step to protect Funso given the circumstances. The Club fully recognises that mistakes happen.
"We are dismayed that the Scottish FA, despite their sympathy with the Club and the player, have not taken a common sense approach, that in this case would have been unlikely to be disputed by anyone in football. They have instead chosen to stick rigidly to the rules which prevent any meaningful discussion to remedy this when we believe it would have been within their discretionary powers to do so."
AFC deliberated with the SFA late into Tuesday this week before a final decision was made.
The Club say they did not ask for the yellow card to be immediately rescinded, but asked for the right to appeal to the Judicial Panel under what would have to be an emergency rule amendment.
AFC Chairman, Dave Cormack, added: "While the SFA have been sympathetic they were not willing to take any action mid-season that would provide us with the opportunity to appeal the yellow card to the Judicial Panel. We have been advised that they will explore a rule amendment for next season, which we welcome, but which won’t help the Club and Funso this time.
"Naturally, we are very disappointed with this outcome because we believe that discretionary powers can and should be used to address and remedy rare situations such as the one in which we found ourselves last Saturday.
"In going through this process, it has been refreshing to know that Bobby Madden and the refereeing fraternity wanted to come out publicly and accept they got this decision wrong. A stronger relationship between clubs and referees, one where Scottish football is open to change and transparency with supporters, can only be seen as a positive step."