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In a speech in London, the ex-PM said he believed the party could have kept much of the vote in traditional Labour areas under a different leadership.
The situation was "made impossible by failure to take a clear position and to stick to it", Mr Blair said.
"The result has brought shame on us. We let our country down," he added.
In an interview with the BBC's Newsnight, to be aired later, Mr Blair said "the Labour Party, by its self-indulgence - and that's what it was in the end - was the effective handmaiden of Brexit.
"It's not our fault, because the fault is with those who advocated it - but our combination of misguided ideology and utter incompetence allowed it to happen."
Jeremy Corbyn told MPs on Tuesday that he "took responsibility" for Labour's worst electoral performance, in terms of seats won, since 1935. [...]
Related article on The Independent: Nearly twice as many Labour voters defected over Jeremy Corbyn's leadership than party's Brexit stance, poll finds
Related article on Verfassungsblog: The Failure of the Left to Grasp Brexit