Ireland were beaten on aggregate in Paris when an extra-time goal by William Gallas had been handled by Thierry Henry.
Former Arsenal striker Henry admitted he had kept the ball in play with his hand, but the act went unpunished, leading to a furious reaction.
End of the world: Ireland goalkeeper Shay Given sits dejected at the final whistle in Paris
Handball: Thierry Henry
Assistant manager Liam Brady and midfielder Kevin Kilbane have led the calls for FIFA to throw out the result and order the match to be played again.
'Well, I'd like to think it would be replayed and I think everyone in the squad would like it replayed,' the Hull City midfielder told talkSPORT.
'You see for yourself he's handballed it once and it's still going out of play so he's handled it again to make sure it doesn't go out of play.
'And you know what? I asked him on the pitch, "did you handball it?" and he said, "yes, but I didn't mean it".
'But when I've seen the replay it's there for all to see that we were let down. It's a massive disappointment for us all here.
'I saw it clear as day. I went over to the referee after the game had finished and I asked him what happened and if he'd seen the handball. He said, "I can 100 per cent say it wasn't handball".
Decision of the Referee - Law 5 of the Laws of The Game state.
The decisions of the referee regarding facts connected with play, including whether or not a goal is scored and the result of the match, are final. The referee may only change a decision on realising that it is incorrect or, at his discretion, on the advice of an assistant referee or the fourth official, provided that he has not restarted play or terminated the match.
'When he said that to me I knew full well that he hadn't even seenit. That was the worst thing about it, we feel really hard done by.'
The 32-year-old admits it will be difficult to bear seeing the World Cup groups drawn in Cape Town on December 4.
Assistant manager Liam Brady believes referee Martin Hansson succumbed to pressure in awarding the decisive goal.
Bradyquestioned the decision by FIFA to seed the play-off draw by worldranking when it looked as though established European powers such asFrance and Portugal plus Germany or Russia could be involved.
Foul play: Kevin Kilbane (left) appeals for handball as William Gallas heads the crucial goal
HAVE YOUR SAY. Have you lost all respect for Thierry Henry? France star Thierry Henry blatantly cheated with his handball that helped his country reach the World Cup finals at the expense of Republic of Ireland. The forward earned a reputation as one of the greatest players to ever grace the Premier League with class on and off the pitch. But is that now overshadowed by his act of cheating? TELL US WHAT YOU THINK He claimed that showed an obvious desire from football's world governing body to ensure the big names qualified, and that Swedish official Hansson felt under pressure to make that happen.
'I wouldn't blame Thierry Henry for what went on,' the former Arsenal midfielder told BBC Radio Five Live.
'I would maybe look at what happened three months before and the fact that these seedings for the play-offs were made to favour the bigger teams. I would ask why that went on.
'The pressure on referees is enormous then. The pressure is too much to bear and I thought the referee up until then had refereed the match in fine fashion, but he succumbed under pressure.'
Caught in the middle: Liam Brady (centre) shields the officials from his furious Ireland players
Brady questioned Henry's assertion that he did not intentionally handle the ball, but he does not blame the Barcelona forward for his actions.
'When you look at the film I think he kept the ball in play and he meant it,' said Brady. 'I wouldn't go down the road of (calling it) cheating, the players seek every advantage they can.
'But I would ask FIFA, "do we want to play the match again?" We would go to Paris and play again. I don't think it would come to that but we would be willing to go to Paris, on their home ground, and have a fair winner.'
Skipper Robbie Keane claimed FIFA president Sepp Blatter and his UEFAcounterpart Michel Platini would be 'delighted' with the 1-1 draw,which gave France a 2-1 aggregate win.
Ecstasy and agony: Robbie Keane scores Ireland's goal against France, but still finished the match disappointed (below)
'They're all probably clapping hands, Platini sitting up there on the phone to Sepp Blatter, probably texting each other, delighted with the result,' said the Tottenham forward.
Henry admitted the ball had struck his arm and claimed he told the referee what had happened.
The Barcelona forward said: 'The ball hit my hand, I will be honest. It was a handball, you can clearly see it. (Sebastien) Squillaci went to jump with two Irish players, I was behind him and the next thing I know the ball hit my hand.
'It was a handball, but I'm not the ref. I told (the referee) but he said to me the same, "you are not the ref".'
The Irish justice minister Dermot Ahern has added to the calls for a replay.
'They probably won't grant it as we are minnows in world football but we should put the powers that be in the cosy world of FIFA on the spot and demand a replay,' he said.
'It's the least we owe the thousands of devastated young fans around the country. Otherwise, if that result remains, it reinforces the view that if you cheat you will win.'
A FIFA spokesman said: 'FIFA is not in a position to comment on decisions taken by match officials.'
VIDEO: Reaction to controversial clash.
Hand of God II: France striker Thierry Henry confesses he cheated to rob Republic of Ireland of World Cup place France 1 Ireland 1 (aet): Luck of the Irish runs out after Gallas goal ends dreamGraham Poll: Cheats never prosper? Well, France certainly did in ParisVIDEO SPECIAL: Thierry Henry joins Diego Maradona, Lionel Messi and Sergio Aguero among others in football's handballing cheats hall of fameHAVE YOUR SAY: Have you lost all respect for Thierry Henry?
Explore more:People:Robbie Keane, Martin Hansson, Shay Given, KEVIN KILBANE, Liam Brady, Thierry Henry, WILLIAM GALLASPlaces:Paris, Cape Town, Barcelona, Ireland, Portugal, Republic of Ireland, Russia, France, Germany