In keeping with her openly pro-choice position, Clinton called the ruling "a serious breach of a woman's right" and told Compton it's time for the other branches of government to step in.
"There has to be some action taken, in the Congress or by the executive to try to clarify what the court just did," she said.
During the interview, Clinton and Compton also discuss the surge of illegal immigration into the United States from Central and Latin America, Clinton's health, her new memoir and how she feels about being a grandmother.
Clinton took the chance to offer President Barack Obama advice about where to find space to let Malia -- who just turned sixteen -- practice driving.
"If you pass along to the president that going up to Camp David worked for us, maybe he can try it now," she said.
Compton and Clinton also discussed the former first lady's astronomical speaking fees, for which she's been criticized after making comments about being broke early in her book tour.
Clinton told Compton the exorbitant fees she commands -- more than $200,000 in most cases -- are donated directly to her family's foundation.
Recently students at the University of Nevada threatened to protest Clinton's scheduled appearance at a fundraiser for the school in October unless she returns her $225,000 fee to the University.
"All of the fees have been donated to the Clinton Foundation for it to continue its life-changing and life-saving work. So it goes from a foundation at a university to another foundation," Clinton claimed.
Despite demanding close to a quarter of a million dollars to make an appearance, Clinton said she believed her speaking tour across the country was actually helping to reduce income inequality.
"It's been my experience that they're not worried about my speaking or my household," she said. "They're worried about their own. And that's the kind of debate I think I'm furthering as I go around the country speaking."