FAI President John Delaney has urged FIFA to uphold their own principles by agreeing to replay Wednesday night's controversial World Cup play-off defeat by France.
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The FAI has lodged a formal complaint with the world governing body, claiming the integrity of the game has been damaged after French forward Thierry Henry blatantly handled the ball during extra-time in the lead-up to the winning goal scored by William Gallas.
"I really believe the integrity of the game has been questioned last night," Delaney said.
"The governing body of world football have to step up to the plate and accede to our call for a replay."
Delaney also confirmed the FAI have written to their French counterparts.
"We have got to do what we have to do," he said.
"We owe it to the players, who were magnificent last night. The supporters were incredible.
"It is up to the people who govern the game now. Every time I go to a FIFA congress I hear about fair play and integrity.
"This was not a league game. This was a defining game with the whole world watching and if FIFA believe in fair play and integrity, this is their opportunity to step forward."
Taoiseach Brian Cowen has said he would raise the controversy with President Nicolas Sarkozy at a European summit.
"I think that fair play is a fundamental part of the game," the Taoiseach said in Brussels.
It is estimated that World Cup qualification would have been worth 30 million euros (£26.7 million) to Irish football.
Ireland's Justice Minister Dermot Ahern and assistant Republic of Ireland coach Liam Brady have also called for the game to replayed.
However, a FIFA source has said: "There is no way the game can be replayed.
"To do so would cause absolute chaos for football. If it was replayed, then every match in the future would also be subject to these calls for a replay any time a referee misses an incident.
"FIFA's rules are absolutely clear. Law five states that a referee's decision on points of fact are final. That is the end of it. You cannot replay the match on this basis."
The FAI believe there is a precedent for the result to be struck out.
FIFA ordered Uzbekistan to replay Bahrain in a play-off for the 2006 World Cup in Germany after the referee made a mistake after a penalty had been awarded.
The governing body described it as a "technical error".
But the referee was guilty of wrongly applying the rules rather than missing an offence.
'Bitter'
Ireland manager Giovanni Trapattoni believes there is no prospect of the match being replayed, telling a press conference in Dublin: "I know it's impossible to replay the game."
Trapattoni has urged FIFA to explain their choice of referee for the game.
"All fans saw what happened on the pitch.
"I would only like to say I would like FIFA to explain how they selected the referee for this important game. For this important game we needed a stronger referee - an important referee."
The Italian continued: "I would give the advice to FIFA - maybe in the future change the rules about the play-off. Play two games and at the end of 90 minutes - no extra-time.
"I will go to FIFA and advise them 'go straight to penalties'. It's better for football."
Trapattoni admitted it had been a "bitter" experience and for him the circumstances of the play-offs were questionable.
He added: "For me it's bitter. There are many questions - they changed the rules about the seeded teams, then us playing away last.
"Out of the non-seeded teams we were the only ones to play the second game away - why?"
But Trapattoni did absolve Henry, saying: "It wasn't up to Henry to say 'I touched it with my hand'."
FIFA confirmed that they have received an official complaint from the FAI.
The spokesman was unable to give a timescale on any decision.
© Press Association