"It worries me a great deal," Feinstein told CNN's Manu Raju. "You know, I don't want to go back to the '68 convention, because I worry about what it does to the electorate as a whole -- and he should, too."
Her comments were the latest evidence that Democrats are increasingly fretting that the divide between supporters of Sanders and backers of Hillary Clinton will be difficult to bridge in time for November's general election.
Earlier Wednesday, California's other Democratic senator, Barbara Boxer, said Sanders supporters should attempt "to change the primary process, but not to go out there and throw chairs and to put people's lives in danger because the democratic process as put forward and ratified by the two parties is being carried out."
Boxer said she felt threatened after outbursts and threats at the Nevada Democratic Convention from supporters of Sanders over the weekend.
"I feared for my safety and I had a lot of security around me," she told CNN's Kate Bolduan on "At This Hour." "I've never had anything like this happen."
After Sanders supporters thought the Nevada Democratic Convention was being shut down prematurely, shouting ensued and there were reports of chairs being thrown. The phone number and address of the chairwoman of the Nevada Democratic Party, Roberta Lange, was posted on social media -- prompting a flood of more than 1,000 calls, angry voicemails, text messages and even death threats.
"It was a scary situation," said Boxer, a Clinton supporter. "It was frightening. I was on the stage. People were six feet away from me. If I didn't have a lot of security, I don't know what would have happened."
Boxer said she expressed her concern to Sanders in a phone call Tuesday night. Sanders released a statement Tuesday to say that he does not support violent behavior from his supporters, but also sharply criticized the convention process from Nevada's Democratic party.
"He knows how I feel. He knows that I felt threatened. He knows that it was wrong," Boxer said. "Now we will see, but in my mind when he says he does not support any type of violence, I believe him. And he's got to make sure it doesn't happen. People will follow his lead."
Boxer wasn't the only Democratic senator to condemn Sanders' supporters behavior over the weekend. Virginia Sen. Tim Kaine slammed Sanders' statement in response to the outbursts.
"What he did yesterday was sort of say it's the party's fault," Kaine told CNN. "That deflection of responsibility is not leadership."
On Tuesday, the Nevada Democratic Party sent a formal complaint to the Democratic National Committee, saying Sanders backers and campaign officials "actively incited disruption and violence" at the convention.
Boxer said she told Sanders the vast majority of his supporters "were fine."
"He was very distressed about it," she said of Sanders' reaction to her on the phone. "He expressed shock his people would do it."
White House press secretary John Earnest on Wednesday warned against reading too much into the tensions and seemed to dismiss Feinstein's concerns.
He said he's not worried about violence at this stage and recalled a similar "tenor" to the 2008 contest between Clinton and then-Sen. Barack Obama. Those tensions were "no less intense" and didn't lead to a negative result in the general election, he added.
"I think one of the lessons of 2008 is not to confuse passion in primary for disinterest in the general election," Earnest said, adding that "highly motivated" supporters were good for democracy.