"The result of the match cannot be changed and the match cannot be replayed," FIFA said in a statement. "As is clearly mentioned in the Laws of the Game, during matches, decisions are taken by the referee and these decisions are final."
Swedish referee Martin Hansson failed to call a handball on the play that led to William Gallas' overtime goal despite fervent appeals by Irish players. Television replays showed Henry touched the ball twice with his left hand before kicking the ball in the direction of Gallas' head.
"Of course, the fairest solution would be to replay the game but it is not in my control," Henry said in a statement issued to British media. "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. There is little more I can do apart from admit that the ball had contact with my hand leading up to our equalizing goal and I feel very sorry for the Irish."
The game's outcome has sparked outrage in Ireland and France.