"I believe that
the time has now arrived when I should bring to a conclusion the continuing
speculation with regard to my participation in the World Cup and for the
players to concentrate fully on their preparations for the competition free
from all further distraction.
"I do not consider that the best interests of Irish football will be served by my returning to the World Cup.
"The damage has been done.
"I wish the team and the management all the best
and they will have my full support throughout the competition.
"I urge all the people of Ireland to give their entire support to the team.
"I do not feel that any useful purpose will be served by my making any further comment.
The Football Association of Ireland's acting general secretary John Byrne said efforts to broker a peace deal had continued "up until seven o'clock tonight".
And he confirmed that an apology from Keane would have been enough to solve the dispute.
"I'd be speculating as to how close he came (to apologising) but we did feel this afternoon he could be on his way back," said Byrne.
"Unfortunately it hasn't worked out. It's unfortunate for Roy, it's unfortunate for the FAI, it's unfortunate for the country but we now have to draw a line in the sand and get on with it."
McCarthy had confirmed on Tuesday that he would consider taking Keane back - but only after an apology, and if the players agreed.
The players later indicated that they would have been happy to have Keane back on board.
"We worked strenuously to resolve the situation. People have made huge efforts to get Roy Keane back to the World Cup," added Byrne.
"Unfortunately it has come to this and I think it is now time to get on with the business of winning our game on Saturday."