France captain Thierry Henry has admitted replaying the World Cup qualification play-off against the Republic of Ireland would be "the fairest solution".
The Barcelona forward has also spoken of his "embarrassment" at the manner of Les Bleus' victory over the Irish.
"Naturally I feel embarrassed at the way that we won and feel extremely sorry for the Irish who definitely deserve to be in South Africa," said Henry, whose handball in the build-up to William Gallas' equaliser on Wednesday night enabled the French to go through 2-1 on aggregate.
"Of course the fairest solution would be to replay the game but it is not in my control."
The Football Association of Ireland (FAI) had formally requested a replay but FIFA earlier today ruled that the result cannot be changed and the match cannot be replayed.
The French Football Federation believe they 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."
Referee Martin Hansson broke his silence today by insisting "life must go on" after failing to spot Henry's handball.
Hansson has since been widely condemned for his mistake but he is hoping to put the incident behind him.
He told Swedish regional radio channel Radio Blekinge: "I cannot comment on the game itself but life must go on and I hope I will survive this too."
Reports have suggested Hansson will still make FIFA's list for next summer's World Cup finals in South Africa.
"Really? Has it been in the evening papers? Well, then it has to be true, hasn't it?" he said with a hint of sarcasm.
France's dismal performance in the play-off, meanwhile, has given Raymond Domenech's critics more ammunition, but the FFF insist he will still be at the helm next summer.
"We qualified," added the spokesman. "For sure he will be our coach.
"When you manage a team and win you don't change the coach. Sometimes you do in club football but not in an international team."
Thierry Henry's statement in full
"I have said at the time and I will say again that yes I handled the ball. I am not a cheat and never have been.
"It was an instinctive reaction to a ball that was coming extremely fast in a crowded penalty area.
"As a footballer you do not have the luxury of the television to slow the pace of the ball down 100 times to be able to make a conscious decision.
"People are viewing a slow motion version of what happened and not what I or any other footballer faces in the game.
"If people look at it in full speed you will see that it was an instinctive reaction.
"It is impossible to be anything other than that. I have never denied that the ball was controlled with my hand. I told the Irish players, the referee and the media this after the game.
"Naturally I feel embarrassed at the way that we won and feel extremely sorry for the Irish who definitely deserve to be in South Africa.
"Of course the fairest solution would be to replay the game but it is not in my control.
"There is little more I can do apart from admit that the ball had contact with my hand leading up to our equalising goal and I feel very sorry for the Irish."