Meath will march on in the All-Ireland Senior Football Championship as Leinster champions but officials admit that their victory is 'tainted' by the controversy surrounding the last minute of the final.
Meath officials also said that more direction should have been provided by Croke Park in the aftermath of the controversy.
The Meath board met last night and a decision was taken not to offer Louth a rematch despite widespread disquiet over the fact that the decisive goal was illegally scored in the dying seconds by Joe Sheridan, who threw the ball over the line.
Among the key factors was the position of the players, who were reluctant to grant a replay.
Crucially, according to a statement released by the Meath county board, Meath would have been awarded a penalty by referee Martin Sludden had Joe Sheridan not taken the ball over the line.
The statement said that Sludden indicated in his report that he 'blew the whistle for a penalty but changed his mind and awarded the goal by Joe Sheridan when he saw that the ball had crossed the line.'
The decision not to grant a replay was taken after discussing the matter with both management and players. It is understood that the management and playing panel were opposed to such an offer.
The statement added: ‘The Executive met for an hour after earlier holding discussions with team management and players. The players had indicated they were not in favour of a re-fixture.
‘The Executive have supported the stance of the players and they say, as far as they are concerned, that is the end of the matter.’
Louth have yet comment on the Meath statement and are still thought to be considering the possibility of taking further legal action.
Speaking to RTÉ Sport's Marty Morrissey, Meath county board secretary Cyril Creaven admitted that the county's 21st Leinster title was tainted and said that more direction should have been provided by Croke Park.
He said: 'I feel we have been put under very serious pressure for something that we had not part in at all. We are very disappointed with the way things out and hence it took us a such a long time to arrive at the decision we came to tonight.’
Louth have received support from across the GAA world but Creaven believes many will empathise with the difficult position Meath found themselves in.
‘I imagine there will be some disappointment at our decision in quite a few quarters but I’m sure there will be others who will see the position we were placed in,' he added.
In future situations, Creaven believes Croke Park should play a more active role in guiding events.
He said: 'We should have probably got a bit more direction from Croke Park. I know the rules are there and we have to abide by the rules but if we proposed a re-fixture we would surely be breaking some rule or some rule would have to be broken to accommodate that.
'I think in this case we should have got further guidance rather than be placed in the unenviable position we were in.'
Even though Meath progress in the All-Ireland Senior Football Championship as Leinster Champions, Creaven admitted that the county's 21st Delaney Cup would always be remembered for the controversy of its final minute.
‘No doubt it is tainted with all of this. We can’t say it is anything but tainted but we have to go on with it.'