Down GAA has said that Kilcoo objected to the appointment of Paul Faloon as referee for the weekend's senior football final against Burren "on the grounds of perceived bias".
Kilcoo took the matter to Croke Park's Disputes Resolution Authority but their claim - which Down GAA said was "baseless" - was rejected.
However, Faloon subsequently stepped down and David Gough was drafted in as his replacement. Gough informed Down on Sunday morning that he would also be withdrawing.
The game - which Kilcoo won 2-12 to 0-9 to claim their 11th county title in 12 years - was eventually refereed by Brian Higgins.
Faloon's club Drumgath said in a statement on Sunday that they were "extremely disappointed in the turn of events".
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Down GAA added that there should be no right of appeal to the appointment of a referee and that they will examine the matter to consider what measures are required to ensure it does not happen again.
Down GAA statement on Kilcoo vs Burren referee fiasco
"Following yesterday's county senior football championship final, Down GAA wish to address the episode relating to the appointment of the match referee," begins the statement.
"Early last week, Paul Faloon was confirmed as the referee for the fixture. As an intercounty championship match official of considerable standing, his was an appropriate appointment. We regard Paul as one of our best match officials, who has officiated at provincial and national level.
"An appeal against this appointment was then pursued by the Kilcoo club, on the grounds of perceived bias. We regarded this as entirely baseless and were determined to fight for the integrity of the referee and the appointment. A hearing took place on Thursday evening last (heard by the Down Hearings Committee), and the appeal was rejected. Kilcoo then lodged a claim with the Disputes Resolution Authority in Croke Park (the GAA's highest resolution body), requesting interim relief on the matter and proposing, as a possible remedy, postponement of the game for a week if the application were to be successful.
"The DRA claim was heard on Saturday morning and the case put forward by Kilcoo was rejected. This was an entirely satisfactory ruling as it allowed the referee appointment to stand, and we communicated it to Paul.
"We were steadfast in our support of the appointment of Paul Faloon. Not even the notion of postponement would deter us from the clear opinion that everyone should respect his appointment.
"However, in the course of Saturday late morning and afternoon, matters transpired that became increasingly difficult for us to resolve. We were left with the prospect that there may be no referee for the fixture, and as a result, had no option but to appoint an alternative official to referee the game.
"Having deemed it unfair in these circumstances to ask another internal referee to take charge of the fixture, we then asked David Gough and he accepted.
"At 11.30am on Sunday, David advised us that he would be withdrawing, and we respected his decision. Brian Higgins then accepted the appointment as referee.
"Whilst the final took place and we are very grateful to all of yesterday's match officials, this was an extremely frustrating episode. As an Association, we are constantly hearing and stating about the need to respect our match officials. The appointment of Paul Faloon should have been respected and it is disappointing that this was challenged in the way that it was. There should be no right of appeal against the appointment of a referee.
"We will examine this episode and consider what needs to be put in place to ensure that this never happens again."