Hearts were left furious with referee Iain Brines and the Scottish Football Association after failing in their appeal against the sending-off of defender Marius Zaliukas against Aberdeen last Saturday.
Zaliukas was dismissed for supposedly headbutting Dons striker Lee Miller and will now have to serve a three-match ban.
But Hearts believe the Lithuanian international was wrongly dealt with by Brines and also slammed the system of contesting red cards.
A statement on the club's official website said: "Hearts' appeal was based on indisputable television evidence that shows Zaliukas was not, in any way, an aggressor and most certainly did not headbutt Aberdeen player Lee Miller, as had been alleged.
"Pictures clearly show that Zaliukas was, if anything, the victim of the incident with the Aberdeen forward."
A club spokesperson added: "We are dismayed and angered by this decision. It is a complete injustice as there can be no argument to suggest that Zaliukas struck, or even intended to strike, the Aberdeen player.
"We don't believe in an appeal system that dictates that the appeal decision should be left solely with the referee, as is the case at present. We understand that this is also a view shared by some other clubs.
"We are hugely supportive of the job that referees have to do, often in difficult circumstances.
"However, in our opinion, a mistake has been made and it is important that when mistakes are made they are acknowledged and we can all move on.
"That is why we are extremely disappointed that Mr Brines will not find it in himself to acknowledge a mistake that the TV cameras prove to be the case."
Zaliukas, who was also sent off against Celtic last month, will miss Saturday's derby against Hibernian, as well as two further SPL games for breaching the 18-point disciplinary threshold.