Albright made the comment earlier this week while stumping for Clinton, but the Democratic hopeful argued that she wants voters of all genders to make their own choices.
"I think she's been saying that for as long as I've known her, which is about 25 years," Clinton said at the Democratic presidential debate in Milwaukee. 
"But it doesn't change my view that we need to empower everyone — women and men — to make the best decisions in their minds that they can make," she continued.
"I've spent my life working so that women can make their own choices, even if that choice is not voting for me."
Clinton pointed out that Thursday's debate on PBS is the first time women have been a majority on the stage during a presidential primary debate.
"We'll take our progress wherever we can find it," she added.  
The debate comes two days after Sanders trounced Clinton in the New Hampshire primary, following the former secretary of State's razor-thin victory in the Iowa caucuses. 
About 55 percent of female voters in New Hampshire supported Sanders in the primary. But Clinton, who has made women's rights a focal point of her campaign, believes her experience and record on those issues will resonate with female voters.
"I feel very strongly that I have an agenda, have a record that really does respond to a lot of specific needs that the women in our country face," she said Thursday.
"I'm going to keep making that case, But I have no argument with anyone making up her mind about who to support. I just hope by the end of this campaign, there'll be a lot more supporting me."