Missouri Sen. Claire McCaskill, who supports Democratic front-runner Hillary Clinton, said Thursday that she didn't hold it against Bernie Sanders when Nevada's Democratic state convention turned hostile over the weekend, and she called the violent incidents in Nevada "an outlier."

When asked if Sanders was right in saying party leaders unfairly accused him of promoting violence, McCaskill said in an interview on "CBS This Morning," "I kind of agree with Bernie on this one."

"I think that Nevada was an aberration," she said. "I think the millions of Bernie Sanders supporters are not people who want to resort to harassment and threats and throwing chairs. I do believe this was an outlier because I think the millions of people who support him are passionate and inspired by the message Bernie is delivering."

Party leaders who expressed concern over his supporters in Nevada were just "upset" by the violence, says McCaskill, a Clinton supporter.

"When [California Sen.] Barbara Boxer, an icon in the progressive movement, is called vulgar names and booed off the stage and feels threatened and harassed, I think it got a lot of people upset," she said. "You know, passions are high, everyone is tired, it's been an emotional campaign."

While McCaskill called the delegate math for Sanders "pretty unforgiving," she doesn't expect him to drop his presidential bid in response to that.

"I think he's resenting that he's feeling that he has to stop now because the math is so difficult for him, and I think he wants to finish this process, and I respect that," McCaskill said, referring to the number of delegates Sanders still needs to catch up to Clinton's lead. But she did complain that while Sanders is pushing the message that the primary process is "rigged" and "closed" by the party against him, she has a different objection.

"Where Bernie Sanders has done well is caucuses and they are closed," she noted. "You can't go if you're working, you can't absentee vote, you can't mail in your ballot. It is a very closed process and that's the majority of the states he's won -- is the most closed process of all."

Despite the rising tensions within the party, McCaskill said there was "no question" the Clinton campaign would need the support of Sanders backers in the general election, if Democrats are to triumph over Donald Trump, the GOP's presumptive nominee.

"We need to unite behind these issues," she said. "It's the Supreme Court. It's whether or not we're gonna have a religious test to get into this country. It's whether or not we're gonna have a guy that can't decide between noon and 3 o'clock in what he believes in, with the nuclear codes."

The Missouri Democrat concluded with a call for the two party factions to unite: "We've had 13 million votes cast for Hillary Clinton and 10 million for Bernie Sanders. It's time those 23 million come together and convince the rest of the country to follow suit."