"I have learned that trying to explain what happened made it sound to some people like I was trying to excuse it. There are no excuses," she told Muir in Cleveland.
She added, "I take responsibility. I made a mistake. I've apologized, and obviously I wish I could do differently what happened. I certainly would never do that again."
The summary of the FBI's findings from July reads, "Clinton did not recall receiving any emails she thought should not have been on an unclassified system."
FBI Director James Comey has said that three email chains with Clinton included at least one paragraph marked "(C)," indicating that the paragraph contained confidential material.
He has called Clinton's handling of classified info "extremely careless" but said there's no evidence to indicate she knew she was sending or receiving classified info.
Clinton told the FBI that she did not know what the "(C)" meant at the beginning of the paragraphs and speculated it was a reference to paragraphs marked in alphabetical order — something she reiterated in ABC's exclusive interview.
"There were no headers on the thousands of emails that I sent or received. There just weren't, and the FBI has not in any way contradicted that. There were a couple of emails with a tiny 'C' in a parenthesis, which did not have a header saying that means 'confidential' in this circumstance and which the director of the FBI has said and the State Department has said those couple of emails were improperly marked, even with that. So, yes, I take classification seriously, and I think the record shows that I have," she said.
"[Trump] said, 'If I run, I promise I'll release tax returns,'" Kaine said. "This is out there because Hillary said, 'Put it out there. Let the American public see it.'"
ABC News' Mike Levine contributed to this story.