Marius Zaliukas' red card against Aberdeen will stand after the SFA rejected an appeal by Hearts, leaving the Edinburgh club furious with the decision.
Hearts had contested the decision, insisting the 25-year-old was wrongly ordered from the field for headbutting Dons match-winner Lee Miller.
A club spokesman said: "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."
Hearts believe Zaliukas was the innocent party in his altercation with Miller.
A statement on the club's official website, read: "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."
The 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."