The assistant manager told Sky Sports News that the FIFA president had shown disrespect in telling a news conference in South Africa details of a supposedly private meeting with Irish officials.
Blatter revealed on Monday that Ireland had asked to be allowed to join the 32 qualified teams because they felt cheated by a Thierry Henry handball that set up a controversial goal for France in their play-off match.
FIFA have said the request would be impossible to meet.
Brady criticised Blatter for failing to recognise the restrained behaviour of both the Irish players and fans at the playoff in Paris, despite the pain of losing out in such fashion.
"Not one player got booked after that incident, not one player got booked after the match," he said. "There were 20,000 Ireland fans in the stadium, not one fan caused trouble in the stadium in Paris that night and in the city that night.
"I think my country deserves a bit more recognition from Blatter and the way he presented it to the press conference in South Africa yesterday.
"I think the man is a bit of a loose cannon. I think he is an embarrassment to FIFA."
Brady, a former Arsenal and Ireland midfielder, said the Irish federation had believed their meeting was private and confidential but "Mr Blatter is a law unto himself and I thought it was very disrespectful".
The Irishman also accused Blatter of ignoring the Henry handball.
"He never spoke about Henry's behaviour after scoring the goal and how that stands within his campaign to help fair play within the game," he said.
"You can see the goal, Henry celebrates as if he has done nothing wrong. Is that fair play? Hardly."
Brady said Ireland knew all along that there was very little chance of their request being granted but had decided to make it anyway on principle.
"We asked because we wanted them to respond in a measured way and see what they say," he explained.
"After all, Mr Blatter is responsible for the officials, he didn't say anything about the appalling mistake the officials made to miss such a blatant handball."
