Last month Blatter announced, just days after his re-election, that he would step down amid a widespread corruption scandal at the organisation.
He told a Swiss magazine on Thursday the English had wanted him out and had "hatred" of FIFA because "they no longer control football".
Dyke, whose association was set up in 1863 and was the earliest in the world as football first developed in England, did not mince his words in reply.
"He's always disliked me, he hates the British media and doesn’t like the English at all which is fine because we don’t really like him," Dyke told Sky Sports.
"I do think he’s coming up with some rather strange things. He’s probably in a state of shock. This is a man that was triumphant, he thought he was going to run FIFA for four years when actually he only ran it for four days.
"The only thing we can argue and complain about is that FIFA is an organisation that has been corrupted over 40 years. The single most important thing now is to talk about how we reform FIFA and not get Blatter mark II."
Blatter's successor will be chosen at a special FIFA Congress between December and February.
"Until we know who is going to stand then we don’t know who we’re going to support," said Dyke.
"But we’re very friendly with (UEFA president Michel) Platini and supported him in the past. So we’ll see what he decides."
(Writing by Mark Meadows, editing by Tony Jimenez)
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