The Republic of Ireland's hopes of a World Cup reprieve have been dashed.

Both FIFA and the French Football Federation insisting there will be no replay of the controversial play-off against France.

France striker Thierry Henry thinks the "fairest solution" would be to replay the match following his handball in the build-up to the vital goal by William Gallas, but FIFA believe match referee Martin Hansson's decision to award the goal should stand.

The Football Association of Ireland (FAI) were yesterday pondering their next action - though it looks highly unlikely they can appeal to FIFA or take the case to the Court of Arbitration for Sport (CAS) in Lausanne.

Stephen Townley, a London lawyer who also acts as an arbitrator for CAS, said the court would not be able to become involved.

Townley said: "Looking at FIFA's statutes, this would come under violation of the laws of the game, in which case CAS could not pick up the dispute.

The FAI had formally requested a replay but FIFA responded yesterday with a statement saying: "The result of the match cannot be changed and the match cannot be replayed. As is clearly mentioned in the Laws of the Game, during matches, decisions are taken by the referee and these decisions are final."

FIFA's announcement was not a surprise - a senior source at the world governing body said they had no option but to reject the demand.

The FIFA source told Press Association Sport: "There is no way the game can 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 5 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.

"You have to have a rule that says the referee's judgement is always right."

The FFF also believe Ireland should now concentrate on looking ahead.

"FIFA is the ruler of the game and we have to abide by what they say,'' said an FFF spokesman.

"What they decide we have to do and they have ruled it will not be replayed. So we should move on.

"The federation's president and the coach and all of us involved feel that it was a bitter qualification. But we don't decide how we qualify.

"We played poorly and it came down to a referee's mistake, but that's the way it went. It happened on our side, in our favour, but sometimes in history it goes against you."

Republic of Ireland coach Giovanni Trapattoni insisted he will not quit but was still venting his fury at FIFA in Gazzetta dello Sport.

"I would like to know what have I done to (Sepp) Blatter," Trapattoni said.

"If he explains it to me at least I would be calm.

"I often go to schools and speak of fair play.

"Perhaps I am a dreamer. FIFA has violated the rules imposing top seeded teams in the play-offs.

"It's treachery.

"I think even (UEFA president Michel) Platini was against this revolution."

Earlier, Irish skipper Robbie Keane had called on the French Football Federation to heed Henry's acceptance of a replay as the fairest solution.

Keane said: "On behalf of the Republic of Ireland players, I would like to thank Thierry Henry for his statement this afternoon that in his opinion a replay would be the fairest option.

"As captain of the French team, to make such a statement took courage and honour, and all of us recognise that.

"As captain of the Republic of Ireland team, I would also be happy for a replay to happen in the interest of fair play so that whichever team qualifies, can do so with their heads held high.

"We can only hope that the French Football Federation might accept the wishes of both captains in the best interests of the game."

That hope is now dashed.