(CNN) -- Irish football officials have finally conceded that there will be no replay of the controversial World Cup playoff against France.
The Football Association of Ireland appealed to both world governing body FIFA and the French Football Federation after Thierry Henry's blatant handball helped set up the goal from William Gallas that settled the two-legged tie.
Henry even admitted that a replay would be the fairest option, but the FFF refused to entertain the possibility of a rematch after FIFA ruled out such an outcome.
"We regret that despite our best efforts for a replay, which would have restored the integrity of the game in front of a world-wide audience, our calls appear to have fallen on deaf ears at the French Football Federation," FAI chief executive John Delaney said in a statement on Saturday.
"Without doubt, the credibility of fair play has been damaged by this incident in front of a worldwide audience.
"Despite our deep disappointment, we thank our players, the wonderful Irish fans and the Irish public at large for their support, as well as the solidarity of the French people.
"We will continue to call on FIFA to take action to ensure that such damaging examples of cheating are not allowed to recur."
The Republic of Ireland lost the first leg 1-0 in Dublin last weekend but leveled the tie on aggregate through Robbie Keane's first-half goal in Paris on Saturday night.
The match went to extra-time, when striker Henry prevented the ball from going out of play with his hand and then stabbed a short cross for defender Gallas to head the winner.
Swedish referee Martin Hansson and his assistants did not see the offense, even though television replays showed that Henry actually handled the ball twice.
Henry admitted to his foul play after the match, but FIFA insisted on Friday that its rules mean that there could be no replay of the match, meaning that 1998 champions France -- the runners-up to Italy in 2006 -- qualify for next year's World Cup finals in South Africa.