Hillary Clinton Wins California and Clinches Nomination

(CBSNews) BROOKLYN -- Gathered with thousands of her supporters in Brooklyn on Tuesday night, Hillary Clinton marked a historic moment.

"Thanks to you we've reached a milestone," she said, to deafening applause. "The first time in our nation's history that a woman will be a major party's nominee for the president of the United States. Tonight's victory is not about one person, it belongs to generations of women and men who struggled and sacrificed and made this moment possible."

Clinton secured the number of delegates needed for the nomination -- 2,838 including both pledged delegates and superdelegates -- late Monday night, according to a CBS News estimate. But Clinton, and her campaign, waited until Tuesday night to celebrate, as the results of the primaries in New Jersey, California and four other states rolled in.

"Your efforts have produced a strong majority of the popular vote, victories in the majority of the contests, and after tonight, a majority of pledged delegates," she said.

Clinton thanked her opponent in the Democratic primary, Vermont Sen. Bernie Sanders, for running an "extraordinary campaign" that she said has been "very good for the Democratic Party and for America."

Sanders, who campaigned in California on Tuesday, has not conceded the nomination to Clinton.

"I know it never feels good to put your heart into a cause, or a candidate you believe in, and to come up short," she said. "I know that feeling well. But as we look ahead to the battle that awaits, let's remember all that unites us."

Clinton then turned her attention to the presumptive Republican nominee, Donald Trump, who she is on track to face in the general election.

"It's clear that Donald Trump doesn't believe we are stronger together," she said. "He has abused his primary opponents and their families, attacked the press for asking tough questions, denigrated Muslims and immigrants. He wants to win by stoking fear and rubbing salt in wounds."

She added: "And reminding us daily just how great he is."

Clinton called on Democrats, Republicans and independents alike to reject Trump's vision, and instead choose hers.

"This election is different," she said. "It really is about who we are as a nation. It's about millions of Americans coming together to say, we are better than this."