"When I look at some of the inner-city schools, it is no wonder parents feel they have to move their children out," he told the Radio 4 Today programme. "It's just not acceptable.
"We can't tolerate people in the teaching profession who are not up to the job. We have got to make it easier to get rid of heads or teachers who simply can't teach or run a school properly."
Mr Blair's sons attend the London Oratory, eight miles from their former home in Islington. Daughter Kathryn will join Sacred Hart high school in Hammersmith, eight miles from Downing Street, in September.
But Nigel de Gruchy, general secretary of the National Association of Schoolmasters Union of Women Teachers, said: "The attack does nothing for the morale of inner-city teachers or parents."