Ireland lost their play-off 2-1 on aggregate, following William Gallas’ controversial winner.
Gallas headed in the winner after Thierry Henry appeared to twice handle the ball before crossing.
“They’re all probably clapping hands, Platini sitting up there on the phone to Sepp Blatter, probably texting each other, delighted with the result,” Keane said.
“He (Henry) nearly caught it, so it’s a bit of a killer. When you see the reaction of the players, (goalkeeper) Shay (Given) especially, he’s two yards away from it,” he continued.
“You don’t get a reaction like that if he’s not sure it’s a handball. He almost caught it and ran into the net with it.”
Keane also blasted Fifa’s late decision to seed the draw.
“Germany had a chance of being in the (play-offs) as well. With two massive countries there’s no way in a million years is there going to be fair draw,” he said.