Thierry Henry said a replay between France and Ireland would be the "fairest solution" to the controversy surrounding the World Cup playoff.
The striker handled the ball in the build-up to William Gallas's goal in Wednesday's 1-1 second-leg draw with Ireland in Paris, earning France a 2-1 aggregate win and sending them through to next year's finals in South Africa.
"Naturally I feel embarrassed at the way we won and feel extremely sorry for the Irish who definitely deserve to be in South Africa," Henry said in a statement issued on his behalf on Friday.
"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 the ball had contact with my hand leading up to our equalising goal and I feel very sorry for the Irish."
"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," he said.
"I have never denied the ball was controlled with my hand. I told the Irish players, the referee and the media this after the game.
"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," he added.
Henry's statement may have come to late to influence FIFA, who had earlier ruled that the match would not be replayed, despite the controversy.
Responding to demands made by the Football Association of Ireland (FAI) for the match to be restaged, football's world governing body said that it was unable to sanction a replay, stating that under Law 5 of the Laws of the Game the decisions of the referee are final.
