Before the decision, David Cameron had called on Blatter to quit as president.
David Bernstein, Dyke's predecessor as FA chairman, called for high-profile footballers and clubs to speak up against an organisation he describes as a "quasi-totalitarian set-up" that "reminds me of the old Soviet empire".
Writing for The Daily Telegraph, Bernstein says Fifa "has gone beyond the point of ridicule", describing as "laughable" the decision to award the 2022 World Cup to Qatar, "a country with a tiny population, a climate that is absolutely inappropriate for such play".
Bernstein joined calls for the national football associations of Europe to come together to boycott the World Cup. "The competition would be fatally weakened without the participation of Uefa, and this would create the pressure for change that we all want."
David Ginola, the former French international footballer, said Blatter's victory was farcical. "It looks to me we are watching a very bad reality television show," he said.
"People have been arrested, there is an FBI investigation towards Fifa. I mean, I don't know what we're talking about. I saw people standing in the audience applauding! Is it a joke?"