Mr Trump belittled his former political apprentice as an "average" governor, lacking in "loyalty".
Mr DeSantis, 44, won re-election in a landslide in Tuesday's midterms, sealing his status as the Republican party's brightest rising star.
He is widely expected to run for the party's 2024 White House nomination.
But Mr Trump, 76, looks increasingly likely to stand in his way.
The former president - who has a massive campaign war chest and remains hugely popular with the party's base - would be a formidable opponent for Mr DeSantis, or any other Republican who dares challenge him.
In a lengthy statement on Thursday night, Mr Trump dismissed the Florida governor as a political lightweight who had come to him "in desperate shape" when running for his first term in office in 2017.
"Ron had low approval, bad polls, and no money, but he said that if I would Endorse [sic] him, he could win," Mr Trump said. "I also fixed his campaign, which had completely fallen apart."
He went on to complain that Mr DeSantis - whom he is nicknaming "Ron DeSanctimonious" - was "playing games" by refusing to rule out a presidential bid.
"Well, in terms of loyalty and class, that's really not the right answer," Mr Trump added.
The former president is widely expected to announce his own plan for a White House comeback as soon as next week.
While Mr DeSantis is bathing in the glow of his re-election victory, Mr Trump has been blamed for the Republicans' disappointing performance in the midterm elections.
The race for control of the House of Representatives and Senate went down to the wire. Two days after Americans went to the polls, it remains unclear which party will control the twin chambers of Congress.
Voters by and large rejected candidates who backed Mr Trump's baseless claims of election fraud in 2020, and many of his high-profile picks for office struggled or lost outright.
Even close allies of the ex-president have called for him to reconsider what he has teased to be a big announcement on 15 November.
"Republicans have followed Donald Trump off the side of a cliff," one former Trump adviser, David Urban, told the New York Times.
"I think he needs to put it [his campaign announcement] on pause," Kayleigh McEnany, Trump's former press secretary, told Fox News.
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