The club appealed the IFA's decision not to impose a penalty on Carrick Rangers after then manager Gary Haveron incorrectly served a ban.
A successful appeal would have left Carrick relegated and Warrenpoint in a promotion/relegation play-off.
The decision means Ballinamallard and Institute will meet in the play-off second leg on Wednesday (19:45 BST).
An IFA Disciplinary Committee opted not to punish Carrick, despite finding that their former manager Haveron had not properly served a touchline ban.
The committee said it was exercising its discretion in the matter.
Haveron sat out a three-game ban handed out by the IFA, but was in the dugout for his club's match against Dungannon Swifts on 23 April when he should not have been.
Carrick faced a possible three-point deduction and relegation from the top flight, plus a possible fine of at least £350, if the outcome of the hearing had not gone in their favour.
The play-off first leg, which Ballinamallard won 2-1 at the Riverside Stadium, took place on 6 May with the second leg delayed until the relegation controversy was resolved.
Warrenpoint Town's appeal against their Premiership relegation has been rejected after an arbitration hearing.