France captain Henry has admitted he handled the ball in an incident on Wednesday which enabled France to qualify for next year's World Cup at the expense of Ireland.
Keane told a televised news conference on Friday: "France were there for the taking and Ireland didn't do it. Same old story.
"They can complain all they want but France are going to the World Cup. Get over it.
"If I'd been there in the dressing room after the game, I wouldn't be talking about the handball. I'd focus on why the defenders didn't clear it. They should've cleared it.
"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? These are skills and lessons you learn as a schoolboy.
"Ireland had their chances in the two games and they never took them but it's the usual FAI (Football Association of Ireland) reaction - 'we've been robbed, the honesty of the game...' It's rubbish."
Keane has never seen eye to eye with Irish soccer officialdom and walked out of the squad on the eve of the 2002 World Cup over his frustration at what he considered sub-standard preparations.
The former Manchester United midfielder also pointed out that Ireland had benefitted from a controversial penalty in their favour in a 2-1 qualifying win over Georgia.
"It was one of the worst decisions I've ever seen which changed the whole course of the game," he said.
"I don't remember the FAI after the game saying we should give them a replay."
