The Irish FA has dismissed appeals from Ballinamallard and Warrenpoint against a decision not to punish Carrick's failure to implement a touchline ban.
The IFA "exercised its discretion" in not imposing a sanction, which could have seen Carrick deducted three points and relegated as the bottom club.
Instead, Warrenpoint finished bottom with the Mallards in the play-off.
The IFA said their appeals had no standing as they were "third parties" to the case involving Carrick.
Gary Haveron, who was Carrick manager last season, sat out a three-game ban handed out by the IFA.
However, he was in the dugout for his club's match against Dungannon Swifts on 23 April when he should not have been there - Carrick were subsequently charged.
In response to the IFA's decision not to punish Carrick, Warrenpoint said they were "shocked" and claimed the ruling body had not been objective.
The chairman of the IFA's Disciplinary Committee explained on Saturday that the right to appeal related to a charge "imposed upon him or it".
The charge was against Carrick only and not involving Warrenpoint and Ballinamallard, even though they were directly affected by the outcome.
The latest decision leaves Warrenpoint relegated, but the club's board has "agreed to go to the next stage which is to pursue Sports Arbitration".
Ballinamallard will now play the second leg of the promotion/relegation play-off against Institute.
The first leg was contested over three weeks ago, with the Mallards winning 2-1, and a date for the second leg has yet to be confirmed.