The Football Association of Ireland has expressed its 'deep disappointment' that the World Cup qualifier with France will not be replayed.
Following Thierry Henry's controversial handball in the build-up to William Gallas' extra-time winner in Paris on Wednesday, the FAI, Ireland captain Robbie Keane and even Henry himself have called for the game to be played again.
However, Fifa have ruled that out and the French Football Federation has also confirmed they are not willing to play the match for a second time.
A number of high-profile figures have demanded that the French should offer a replay, including Arsenal's French boss Arsene Wenger, while chief executive of the FAI John Delaney has expressed regret that the FFF have decided to ignore the requests.
"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," he said in a statement.
"Without doubt, the credibility of fair-play has been damaged by this incident in front of a world-wide 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."
Fifa had previously rebuffed the Irish appeals to replay the match despite the mass outrage.
A statement on their official website read: "As is clearly mentioned in the Laws of the Game, during matches, decisions are taken by the referee and these decisions are final."