Mr Powell said he could not understand why more preparations had not been made, in an interview to be broadcast on US television on Friday.
A new opinion poll by the Pew Research Center suggests two-thirds of Americans think President George Bush could have done more in the disaster aftermath.
US Under-Secretary of State Karen Hughes backed the president's response.
She said allegations that he was not doing all he could to help were heartbreaking to him.
'Blinding obvious'
American political figures in both the Republican and Democrat parties have criticised the slow response to the disaster.
The BBC's Justin Webb in Washington says Mr Powell's views will be listened to with particular interest - as a highly respected figure and a prominent black American.
Mr Powell told ABC there had been "a lot of failures at a lot of levels - local, state and federal".
"There was more than enough warning over time about the dangers to New Orleans. Not enough was done," he said.
The Pew Research Center poll indicated that two-thirds of the African-Americans questioned believed the government reaction would have been faster if most of those affected had been white.
But Mr Powell said so many African-Americans were left unprotected because they were poor, rather than because they were black.
It "should have been a blinding flash of the obvious... that when you order a mandatory evacuation, you can't expect everybody to evacuate on their own", he said.
Mr Powell's interview comes amid a growing partisan rift over the form of an inquiry into the government response.
Democratic leaders said they would refuse to appoint members to a committee that Republican leaders plan to create.
Republicans said they would aim to go ahead, despite the threatened boycott. One accused the Democrats of seeking to score political points in the aftermath of the disaster.
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