Keane has had a poor relationship with the FAI since his walk-out from the Republic of Ireland training camp ahead of the 2002 World Cup.
He told a press conference broadcast by Sky Sports News: “I think the supporters deserve better, the manager (Giovanni Trapattoni) deserves better and probably most of the players deserve better, but I’m not sure the FAI deserve better.
“What goes around comes around.”
He added: “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…’
“There was one match against Georgia where Ireland got a penalty and it was one of the worst decisions I’ve ever seen which changed the whole course of the game.
“I don’t remember the FAI after the game saying we should give them a replay.”
Keane blamed Ireland’s defence rather than Henry for France’s controversial winner.
“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?”
He added on the 2002 World Cup: “People seem to forget what was going on in that World Cup, and that man (FAI chief executive John Delaney) is on about honesty. I was one of the players and he didn’t have the courtesy to ring me.
“I’d been involved with Ireland since I was 15 years of age and that man didn’t have the decency to make a phone call. He could have phoned me, of course he could have.”
