An IFA Disciplinary Committee opted not to impose any sanction after finding that Carrick did not properly implement manager Gary Haveron's touchline ban.
The committee said it would "exercise its discretion" in the matter.
A Warrenpoint Town statement argued that the decision "contradicted the IFA's obligation to apply objectivity".
"The board of Warrenpoint Town have read the IFA Disciplinary Committee determination regarding the breach of Article 23.1 of the IFA Disciplinary Code by the Carrick Rangers FC Manager," the statement began.
"We are shocked that the IFA having found Carrick guilty failed to implement the requisite admonishment as per established rules.
"The board will be meeting soon to discuss further this matter and the complaint we formally raised surrounding eligibility which is in abeyance."
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 did not go in their favour.
However in a statement released on Wednesday night, the committee indicated that "the interests of justice were best served by not imposing a sanction in all the circumstances".
As it stands, Ballinamallard United and Institute await a date for the second leg of their promotion-relegation play-off, the Mallards having won the first leg 2-1 at the Riverside Stadium on 6 May.
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.
"The club did not explain to the Committee's satisfaction the reasons why the start date for the suspension set out in the initial charge letter (18 April 2016)  was not complied with and therefore the challenge from Carrick Rangers was not upheld," read the IFA statement released on Wednesday night.
"The Committee took into account the points made on behalf of the club and decided to exercise its discretion under the overriding objective as outlined in Articles 1.6 and 1.7 of the Disciplinary Code and found that no sanction should be applied."
"In applying its discretion it took into account, what it found to be the honest intention of the club to serve a suspension, the fact that three matches had been served and points made regarding possible confusion in the way in which the suspension was to be implemented."
Warrenpoint Town say they are "shocked" by an IFA ruling that confirmed their relegation from the Premiership and saw Carrick Rangers stay in the top flight.