Mrs Clinton, 69, said it was hard to listen to her rival's inauguration speech, which she slammed as "a cry from the white nationalist gut".
He painted a dark picture of "American carnage" and the necessity to clean up crime and unemployment in a broken United States.
But his rival gave him credit for appealing so successfully to disillusioned white voters.
"He was quite successful in referencing a nostalgia that would give hope, comfort, settle grievances for millions of people who were upset about gains that were made by others," she said.
"What you're saying is millions of white people?" asked host Jane Pauley.
"Millions of white people, yeah. Millions of white people," said Mrs Clinton.
She added: "A lot of people didn't want to hear my plans. They wanted me to share their anger. And I should've done a better job of demonstrating I get it."
The Democrat and first female presidential nominee of a major US party said she was "done with being a candidate", but she said she would remain active in the political sphere because "our country's future is at stake".
She also spoke again about the presidential debate in St Louis, when Mr Trump stood close behind her as she spoke. "My mind is going, 'OK, do I keep my composure, do I act like a president, am I the person people can trust in the end to make hard decisions?' Or do I wheel around and say, 'Get out of my space, back up, you creep'?"
Mrs Clinton says she takes full responsibility for losing the presidential election, writing: "I go back over my own shortcomings and the mistakes we made. I take responsibility for all of them. You can blame the data, blame the message, blame anything you want - but I was the candidate. It was my campaign."
But she also spoke about Russian election interference, and the decision by then-FBI director James Comey to reopen an investigation into her emails. "It raised the spectre that, somehow, the investigation was being reopened. It just stopped my momentum," Mrs Clinton said.
"At the same time he does that about a closed investigation, there's an open investigation into the Trump campaign and their connections with Russia," she said.
"You never hear a word about it. And when asked later, he goes, 'Well, it was too close to the election.' Now, help me make sense of that. I can't understand it."
Moscow has denied meddling in the US election, and Mr Trump has denied his campaign colluded with Russia.
"Maybe I missed a few chances," Mrs Clinton said, naming using a personal email account as her biggest mistake.
Despite the Comey announcement, however, Mrs Clinton said she had not thought she might lose and never drafted a concession speech.
"The forces that were at work in 2016 were unlike anything that I've ever seen or read about," she added. "It was a perfect storm."