In a brief interview with The Associated Press, Clinton was questioned about Ferraro's remarks. The Obama campaign has called on the New York senator to denounce them.
Ferraro told the Daily Breeze of Torrance, Calif.: "If Obama was a white man, he would not be in this position. And if he was a woman (of any color) he would not be in this position. He happens to be very lucky to be who he is. And the country is caught up in the concept."
The newspaper published the interview last Friday.
Clinton said, "I do not agree with that," and later added, "It's regrettable that any of our supporters - on both sides, because we both have this experience - say things that kind of veer off into the personal."
"We ought to keep this on the issues. there are differences between us" on approaches to health care, energy, experience, she added.
On CBS News' The Early Show Wednesday, co-anchor Harry Smith asked Obama about Ferraro's statements.
"Obviously, I strongly disagree with her comments," Obama said. "I think if you think about the history of this country, the notion that being a black American named Barack Obama paves the way for the presidency doesn't, I think, ring true with most Americans."
Ferraro is a former New York congresswoman and was Walter Mondale's running mate when he was the Democratic presidential nominee in 1984. She has endorsed Clinton and raised money for her campaign.
Obama senior adviser David Axelrod said Ferraro should be removed from her position with the Clinton campaign because of her comments.
"The bottom line is this, when you wink and nod at offensive statements, you're really sending a signal to your supporters that anything goes," Axelrod said in a conference call with reporters on Tuesday.
"There's no other way to send a serious signal that you want to police the tone of this campaign," he added. "And if you don't do those things then you are simply adding to the growing compendium of evidence that you really are encouraging that."
Axelrod said Clinton has encountered problems because people view her as a "divisive and polarizing force."
"The best way to address those concerns is to not allow divisiveness and negativity to flourish among your supporters," he said. "And this is an opportunity for her to address that."
Jan Schakowsky, an Obama supporter and Illinois congresswoman, said Democrats should not tear each other down, and instead focus on defeating John McCain, the Republican nominee-in-waiting.
"I respect every person's right to promote his or her candidate, but any and all remarks that diminish Senator Obama's candidacy because of his race are completely out of line," Schakowsky said on the conference call.
Ferraro also said Obama has it easy because of a "very sexist media."
"I think what America feels about a woman becoming president takes a very secondary place to Obama's campaign - to a kind of campaign that it would be hard for anyone to run against," she said. "For one thing, you have the press, which has been uniquely hard on her. It's been a very sexist media. Some just don't like her. The others have gotten caught up in the Obama campaign."
Last week, a former adviser to Obama resigned after calling Clinton "a monster."