(CNN) -- Thierry Henry believes a replay would be the "fairest solution" after his handball set up France's clinching goal in their World Cup playoff with the Republic of Ireland.
As the controversy showed no signs of abating on Friday, Henry released a statement to news organizations in which he claimed again that he was not a cheat and that his handball had been an "instinctive reaction."
Earlier on Friday, world governing body FIFA denied a request by the Irish Football Federation (FAI) to replay the game, a reality touched upon by Henry in his statement.
"The fairest solution would be to replay the game but it is not in my control," said the Barcelona striker.
"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," Henry added.
"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.
Henry, who touched the ball twice with his hand before crossing for William Gallas to score France's equalizer, putting them 2-1 ahead on aggregate, claimed television technology had made the incident look worse.
"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."
Henry's former Arsenal manager Arsene Wenger told Sky Sports News that the the French federation should offer for the game to be replayed.
"For the sense of justice it is quite embarrassing to see," he said.
"I think even France is embarrassed.
"We didn't play well at all and we won the game and won the qualification with a goal that was not a goal."
But former Ireland captain Roy Keane took the opposite view in an astonishing broadside aimed at leading officials at the FAI, accusing them of hypocrisy and telling them to "get over it."
Keane told gathered reporters: "Ireland had their chances in the two games (against France), and they never took them.
"But it's the usual FAI reaction -- 'we've been robbed, the honesty of the game."
Keane went on to put the blame on the Irish defense for the controversial winning goal.
"I'd focus on why they didn't clear it," he said.
"I'd be more annoyed with my defenders and my goalkeeper than Thierry Henry. How can you let the ball bounce in your six-yard box?
"How can you let Thierry Henry get goal-side of you? "If the ball goes into the six-yard box, where the hell is my goalkeeper?"