Power said: "Last Monday, I made inexcusable remarks that are at marked variance from my oft-stated admiration for Senator Clinton and from the spirit, tenor, and purpose of the Obama campaign.
"I extend my deepest apologies to Senator Clinton, Senator Obama, and the remarkable team I have worked with over these long 14 months."
In an interview with a UK newspaper, Power said that "she [Clinton] is a monster ... she is stooping to anything".
She also said that the Obama campaign "f***d up in Ohio", referring to the midwestern state where he lost to Clinton in Tuesday's primary.
"In Ohio, they are obsessed and Hillary is going to town on it, because she knows Ohio's the only place they can win," Power was quoted as saying.
She also said that she spoke to Obama and "he made it absolutely clear that we could not make comments like this in his campaign".
"I really hope I haven't done him any harm because I know he's been trying to run such a clean campaign," Power said.
She caused a further embarrassment when she said in another interview that Obama may not be able to withdraw all US combat troops from Iraq within a year as he has promised on the campaign trail.
Power told the BBC Obama's position is that withdrawing all US troops within 16 months is a "best-case scenario" that he will revisit if he becomes president.
"He will, of course, not rely on some plan that he's crafted as a presidential candidate or a US senator," Power said.
"[Obama] will rely upon a plan - an operational plan - that he pulls together in consultation with people who are on the ground to whom he doesn't have daily access to now."
Clinton said Power's comment on Iraq was reminiscent of Obama's senior economic adviser telling Canadian officials privately that Obama's criticism of the free trade agreement with Canada and Mexico was "political positioning".
The description appeared in a Canadian government memo.
Clinton said the two instances suggest Obama "keeps telling people one thing, while his campaign tells people abroad something else. I'm not sure what the American people should believe".
But Clinton's campaign too has faced some awkward moments over reports in Canada said an official in her campaign gave Canada back-channel assurances that her harsh words about Nafta were for political show.
The Canadian government and Clinton's campaign has denied the reports.