Speaking to supporters Wednesday at the New Yorker Hotel in Midtown, Clinton said the campaign has been "one of the greatest honors" of her life. She said the effort was not about her, but "the country we love."
She acknowledged that America has not "shattered that highest and hardest ceiling" with her failed bid for the White House. But she said, "someday, somebody will."
"To all the little girls who are watching this, never doubt that you are valuable and powerful and deserving of every chance and opportunity in the world to pursue and achieve your own dreams," Clinton said.
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The nation proved to be "more divided than we thought," the defeated Democratic candidate told supporters.
"This is not the outcome we wanted or we worked so hard for, and I'm sorry that we did not win this election," she said.
Trump was declared the winner after midnight, ending eight years of Democratic control of the White House. He will govern with a Republican-controlled Congress, but he faces fractures within his own party, given the numerous Republicans who wouldn't back him or only tepidly supported his nomination.
With several million votes still to be counted, Clinton held a narrow lead in the nationwide popular vote. Most of the outstanding votes appeared to be in Democratic-leaning states, with the biggest chunk in California, a state Clinton overwhelmingly won. With almost 125 million votes counted, The Associated Press tally had Clinton with 47.7 percent and Trump with 47.5 percent.
President Barack Obama spoke from the Rose Garden Wednesday and said he invited Trump to a meeting at the White House Thursday.
"It is no secret that the president elect and I have some pretty significant differences," Obama said. "But remember, eight years ago, President Bush and I had some pretty significant differences. But President Bush's team could not have been more professional or more gracious in making sure we had a smooth transition so that we could hit the ground running."
Trump has pledged to introduce sweeping changes to U.S. foreign policy, including building a wall along the U.S.-Mexico border. He has praised Russian President Vladimir Putin and advocated a closer relationship with Moscow, worrying some in his own party who fear he'll go easy on Putin's provocations.
Putin sent Trump a telegram of congratulations.
"Putin expressed hope for joint work to restore Russian-American relations from their state of crisis, and also to address pressing international issues and search for effective responses to challenges concerning global security," the Kremlin said in a statement.
Trump was outspent and down in the polls most of the race against Clinton, whom he often called "crooked."
He spoke very differently of his opponent following his win.
"We owe her a major debt of gratitude for her service to our country," he said during his victory speech.
His stances on hot button issues and his rhetoric were points of major criticism as he beat out 16 GOP primary rivals.
In the end, excited white working class men and women and lower turnout from Democrats than 2012 propelled Trump to victory.
"This was a campaign for the people, and they have spoken. They want to go in a new and different direction. They want different leadership," said Kellyanne Conway, Trump's campaign manager.
The Associated Press contributed to this report.