Initial reports showed the Massachusetts senator in fourth place, although results were still in the process of being announced by the time the president posted his tweet blasting the White House hopeful.
“Elizabeth Warren, sometimes referred to as Pocahontas, is having a really bad night,” the president posted to Twitter. “I think she is sending signals that she wants out. Calling for unity is her way of getting there, going home, and having a ‘nice cold beer’ with her husband!"
The message came as Ms Warren insisted she would continue to fight in the 2020 presidential race and has no intention of dropping out.
“Our best chance of beating Donald Trump is with a candidate that will work,” she said earlier Tuesday evening, “a candidate who can build a campaign to unite our party and a candidate who can build a movement who is ready to take on corruption and win.”
Democratic candidates compete on the campaign trail: In pictures
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She insisted she would stay in the race for the White House despite a weak showing in New Hampshire’s first-in-the-nation primary, telling her supporters in a speech: “I am here to get big things done.”
The Massachusetts senator added: “Tonight, I am here to say thank you.”
She delivered the speech as initial results showed Mr Sanders in first place, followed by Mr Buttigieg and Ms Klobuchar, respectively.
An earlier memo the campaign released to staffers and later obtained by multiple outlets cast Ms Warren as the underdog candidate who was primed for a long primary race.
That speech sought to discredit her opponents in the Democratic primaries, which the senator has largely avoided doing along the campaign trail. It said Bernie Sanders had a "ceiling" of support in the race, and suggested Pete Buttigieg would not be capable of building the diverse coalition necessary to win the nomination.
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