Dublin City Council has said its decision on the Garth Brooks concerts cannot be amended or appealed.
In a statement this evening, the council said it had been consistent in informing the promoter that its main concern was the impact that five consecutive concerts would have on the local area.
A number of interested parties today called for a review of the decision to permit only three of the five Garth Brooks concerts.
A group of local residents, who are not affiliated with others, are signing a petition, saying they would be happy for the concerts to happen if the proposals in the Mulvey report are implemented.
The proposals in that report, carried out by Labour Relations Commission Chief Executive Kieran Mulvey, include a cap on concerts in the future and a €500,000 fund for the local community.
Sinn Féin group leader on Dublin City Council, Councillor Seamus McGratten, has also called on the CEO of Dublin City Council to reverse its decision.
Meanwhile, Mr Mulvey who had been engaged as a mediator between the parties described the current uncertainty as "a debacle".
He described the whole process as a "mess", saying that fans who bought tickets should not be the losers.
He suggested that the GAA might offer to not hold any concerts in 2015 in exchange for getting residents to agree to the five Garth Brooks concerts this summer.
However, there is no indication that this will be the case and a solicitor representing one local resident has threatened legal action if the remaining three concerts go ahead.
Anthony Fay has said an injunction will be taken on behalf of a local resident against the Croke Park authorities and Aiken Promotions unless they call off the concerts by next Monday.
Minister for Transport, Tourism and Sport Leo Varadkar said: "The way this happened at the very last minute is clearly unsatisfactory from everyone's point of view and highlights the need to review the major events licencing laws.
"Nonetheless residents have legitimate concerns about five concerts in a row, which the GAA has conceded was a mistake," he said.
"The decision on the licence was made by Dublin City Council and there is no provision in law for it to be appealed or overturned other than by the courts," Mr Varadkar added.
Lord Mayor of Dublin Christy Burke also said he understands the decision not to give permission for two of the planned concerts cannot be changed or reviewed.
Speaking on RTÉ's Today with Sean O'Rourke, Mr Burke said it is a matter for the Dublin City Manager, who was to discuss issues around the concerts today.
Meanwhile, reports that promoters are seeking an alternative venue, such as the Aviva Stadium, for the concerts have been dismissed as there is not enough time for a licence application.
Several venues around the country have said they are prepared to stage the cancelled concerts.
Last night, Garth Brooks himself stated that it is a case of five shows at Croke Park or none at all.
In a statement, Mr Brooks said: "I can't thank the people of Ireland enough for how welcome they have made me feel.
"I have faith that Dublin City Council will make the best decision for the people of Ireland.
"For us, it is five shows or none at all. To choose which shows to do and which shows not to do, would be like asking to choose one child over another." he said.
The council said allowing all five concerts would have caused unacceptable levels of disruption to the local community.
Peter Aiken of Aiken Promotions yesterday said he was disappointed that the local authority denied permission for concerts on Monday 28 July and Tuesday 29 July.
Mr Aiken told RTÉ News that the Croke Park performances had grown from an initial two shows to a much bigger customised production, which would be a once-off event that would not be replicated anywhere else in the world.
The production costs were scaled on this basis and it was not possible to simply stop two of the shows, he said.
Concerts are always promoted on the basis of the concerts being subject to licence.
He said this has always been the way the system has operated in Ireland for any event attended by more than 5,000 people.
Mr Aiken said he did not expect the decision and had been under the belief that even though there may have been a lot of conditions attached, that all of the concerts would be allowed to proceed.
The GAA yesterday said it would assess the implications of the council's decision.