The Football Association of Ireland (FAI) called on FIFA on Thursday to order a replay of the controversial World Cup play-off against France.
France booked their place in next year's finals in South Africa with a 1-1 draw in Paris on Wednesday after striker Thierry Henry handled the ball in the build-up to their goal.
"The blatantly incorrect decision by the referee to award the goal has damaged the integrity of the sport and we now call on FIFA, as the world governing body for our sport, to organise for this match to be replayed," read an FAI statement.
"The hand-ball was recognised (by) the FIFA commissioner, the referee observer and the match officials as well as by the player himself."
The FAI issued the statement as Ireland manager Giovanni Trapattoni was telling a news conference it would be impossible to replay the match.
"I cannot ask this because I know it is impossible," said Trapattoni after his team had gone out 2-1 on aggregate. "When a referee decides, it ends the game for me."
The FAI, though, said there was a precedent for a replay to be staged.
"There is precedent for the invalidation of such results," added the statement.
"In 2005 the bureau of the FIFA World Cup organising committee reached a decision to invalidate the result of a World Cup qualification match between Uzbekistan and Bahrain on the basis of a "technical error by the referee'.
"The Football Association of Ireland is hoping FIFA and its disciplinary committee will, on behalf of football fans worldwide, act in a similar fashion so the standards of fair play and integrity can be protected."
A spokesman for soccer's governing body told Reuters: "FIFA is not in a position to comment on decisions taken by match officials."
