The Highland club's grievances were aired shortly after Rangers said they were leading the charge to change the "flawed" process.
Caley Thistle spoke out after losing their appeal over the second booking and subsequent red card shown to forward James Keatings in the 2-1 Tunnock's Caramel Wafer Challenge Cup semi-final win over Rangers Colts on Sunday.
The 28-year-old was heading for goal when he went down under a challenge from Gers defender Ciaran Dickson but match referee Greg Aitken showed the former Hibs striker a second yellow card and sent him off for two bookable offences.
Inverness says they were "incredulous and furious" about the appeals decision.
In a statement attributed to club CEO Scot Gardiner and chairman Ross Morrison, the club said: "Following the decision by the three-man Fast Track Tribunal Panel to dismiss the club appeal against the yellow card awarded to James Keatings by referee Greg Aitken during Sunday's Tunnock's Caramel Wafer Cup Semi-Final, the club has no option but to speak out publicly on behalf of our player and on behalf of the growing number of Scottish football clubs who believe that the SFA disciplinary process is not fit for purpose.
"In relation to the inexplicable decision to dismiss our appeal this morning, one which will see James miss the Cup Final, we would like to communicate with our support and to the many people who have contacted James and the club since Sunday.
"Our appeal was submitted on Monday morning with our payment for the right to appeal and video evidence of three different angles of the incident, with the most enlightening angle shown at full speed and also in slow motion.
"The referee also submitted his reply to the appeal and within that, he states that from his angle, he believed there had been no contact made by the defender on James and this led him to believe that James had thrown himself to the ground in an attempt to deceive him, therefore he deemed it to be an act of simulation, hence the decision.
"We do not want to question anyone's integrity in this statement and therefore if we set what we do or do not believe aside, it could certainly be argued that this position is plausible.
"The video evidence however removes all doubt from the situation and it was this evidence with which we confidently based our case on. As far as we were concerned, once the three-man panel viewed the video evidence, coupled with the fact that the referee himself was stating that he only made the decision based on his personal view, albeit that he was only a few yards away and not the vastly superior and different video angles, justice and sporting integrity would surely prevail.
"James Keatings has never been booked for simulation in his entire career and Sunday's red card was also the first in his career. The player himself was devastated by the decision on Sunday and has been contacted by many players, ex-players, the PFA and multiple journalists and friends, all of whom believed that justice would be done by the panel. This scenario represented the exact situation that these protocols were set up to address.
"When the club was given the news this morning that the appeal had not only be dismissed but that James had in fact been adjudged to have committed simulation, we were both incredulous and furious in equal measure. We would once again re-iterate that we do not want to call into question anyone's integrity with this statement but we must call into question the actual football knowledge of those sitting in judgment on all Scottish football players under this current system.
"If the individuals involved in this morning's tribunal can watch the footage we supplied, footage which the whole of Scottish football has now seen and call this simulation, then there can be no other conclusion other than they do not understand football or the rules of the game. As harsh as this sounds, there can be no other conclusion. Fans and officials of all clubs are mystified by this decision.
"This decision has cost our player the chance to play in a national Cup Final, not something that comes along every week, to the detriment of the player, his team mates, the club and our fans. We believe it also damages the credibility of our governing body and brings the game into disrepute.
"The decision is plainly wrong and the dogs in the street know this. We have no right to appeal this final decision and it is painful to accept."
Inverness have called on other clubs to support them in their bid to reform the SFA disciplinary system.
The statement added: "As a club we have been contacted by Chairmen, Chief Executives, Directors and fans of other clubs today in a completely unique show of support and solidarity with James Keatings and ICTFC. As appreciated as this has been undoubtedly been, it does not change the fact that there is clearly something wrong with the system, if it is not addressed, we are all responsible for the continuing denigration of our standards, our supporters view of the national game and sporting integrity in Scottish football."
Rangers MD Stewart Robertson had earlier criticised the SFA after his own club were fined over incidents in games against Celtic and Hibs.
"We have been disappointed for quite some time in the way that the disciplinary process is working. We've been quite vocal in that," Robertson said.
"There's also been a lot of lobbying going on in the background for changes and it's good to see other clubs are joining in that lobbying campaign at the moment."