She also addressed her female supporters, who had hoped that she would make history by being elected the first female president.
"To all the women and especially the young women who put their faith in this campaign and in me, I want you to know that nothing has made me prouder than to be your champion. Now, I know, I know we have still not shattered that highest and hardest glass ceiling, but someday, someone will," she said.
That echoes her concession speech during the 2008 Democratic primaries, when she dropped out when it became clear that then-Sen. Barack Obama would be the party's nominee.
Last night Trump praised Clinton in his victory speech, saying the former secretary of state had called to concede. But she did not make any public statements between then and this morning.
She did not address the crowd of her supporters who had waited for hours at the Javits Center in Manhattan on Tuesday night. Instead, Clinton campaign chairman John Podesta made a brief statement shortly after 2 a.m., saying the race in several states was "too close to call" and telling supporters to go home.
Her running mate, Sen. Tim Kaine, introduced her and said he is "excited and proud" of her, saying, "Last night she won the popular vote of Americans."
"That is an amazing accomplishment," he said.
Clinton staffers and donors gathered for her speech at the New Yorker hotel, about half a mile from where she had planned to celebrate a historic victory Tuesday night.