Gates was charged with disorderly conduct. The charge was dropped Tuesday, and Gates has since demanded an apology from Crowley.
Obama was asked about the arrest of Gates, who is his friend, at the end of a nationally televised news conference on health care Wednesday night.
"I think it's fair to say, number one, any of us would be pretty angry," Obama said. "Number two, that the Cambridge police acted stupidly in arresting somebody when there was already proof that they were in their own home. And number three -- what I think we know separate and apart from this incident -- is that there is a long history in this country of African-Americans and Latinos being stopped by law enforcement disproportionately, and that's just a fact."
In radio interviews Thursday morning, Crowley maintained he had done nothing wrong in arresting Gates.
"I support the president to a point, yes, I think it's disappointing that he waded into what should be a local issue and something that plays out here," Crowley told WEEI. "As he himself said ... he doesn't know all the facts."
Crowley did not immediately respond to messages left by The Associated Press on Thursday.
Gates has said he was "outraged" by the arrest. He said the white officer walked into his home without his permission and only arrested him as the professor followed him to the porch, repeatedly demanding the sergeant's name and badge number because he was unhappy over his treatment.
"This isn't about me; this is about the vulnerability of black men in America," Gates said.
He said the incident made him realize how vulnerable poor people and minorities are "to capricious forces like a rogue policeman, and this man clearly was a rogue policeman."
Crowley, 42, said he won't apologize. And his union has expressed "full and unqualified" support for him.
Fellow officers, black and white, say he is well-liked and respected on the force. Crowley was a campus police officer at Brandeis University in July 1993 when he administered CPR trying to save the life of former Boston Celtics player Reggie Lewis. Lewis, who was black, collapsed and died during an off-season workout.
Gates' supporters maintain his arrest was a case of racial profiling. Officers were called to the home by a woman who said she saw "two black males with backpacks" trying to break in the front door. Gates has said he arrived home from an overseas trip and the door was jammed.
The president said federal officials need to continue working with local law enforcement "to improve policing techniques so that we're eliminating potential bias."
Gov. Deval Patrick, who is black, said he was troubled and upset over the incident. Cambridge Mayor Denise Simmons, who also is black, has said she spoke with Gates and apologized on behalf of the city, and a statement from the city called the July 16 incident "regrettable and unfortunate."
The mayor refused Thursday to comment on the president's remarks.
Police supporters charge that Gates, director of Harvard's W.E.B. Du Bois Institute for African and African American Research, was responsible for his own arrest by overreacting.
Black students and professors at Harvard have complained for years about racial profiling by Cambridge and campus police. Harvard commissioned an independent committee last year to examine the university's race relations after campus police confronted a young black man who was using tools to remove a bike lock. The man worked at Harvard and owned the bike.
Richard Weinblatt, director of the Institute for Public Safety at Central Ohio Technical College, said the police sergeant was responsible for defusing the situation once he realized Gates was the lawful occupant. It is not against the law to yell at police, especially in a home, as long as that behavior does not affect an investigation, he said.
"That is part of being a police officer in a democratic society," Weinblatt said. "The point is that the police sergeant needs to be the bigger person, take the higher road, be more professional."
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