He offered his opinions on Mr Trump's proclivity for creating insults out of the governor's last name during an interview with The Pulse of New Hampshire.
"I think it's so petty," he told the programme. "I think it's so juvenile. I don't think that's what voters want."
Mr Trump frequently calls the Florida governor "Ron DeSanctimonious" when disparaging his primary rival.
Mr DeSantis told the radio show that he believes the former president's behaviour was a driving factor in his 2020 loss.
“Honestly, I think that his conduct, which he’s been doing for years now, I think that’s one of the reasons he’s not in the White House now because I think he alienated too many voters for things that really don’t matter,” Mr DeSantis said. “So I don’t get into the gutter on any of that.”
Mr DeSantis has long walked a tightrope when it comes to the former president; while acknowledging that Mr Trump is a rival — and a rival who frequently insults him — he typically hedges his rebuttals to the former president with compliments and shows of solidarity.
The governor decried Mr Trump's indictment as a Democrat-led witch hunt while also noting he was unaware of "what goes into paying hush money to a porn star."
He also criticised the FBI's raid on Mar-a-Lago, which revealed Mr Trump had been hoarding sensitive government documents, calling it a "weaponisation" of government agencies against Democrats' political opponents.
Mr DeSantis recently said he would consider offering Mr Trump a pardon if he is convicted of federal crimes, assuming he wins the presidency.
Even in his interview with The Pulse of New Hampshire, Mr DeSantis notes that while he and Mr Trump have "substantive differences," he still believes the former president "did a lot of great things."
“I still give him credit for the great things he did, but he’s attacking me on policy where we have a disagreement, and I’m the one that’s in the right on this,” he said.
A particular sticking point Mr DeSantis cited was Mr Trump's claim that former New York Governor Andrew Cuomo handled the coronavirus pandemic better than he did.
“Florida boomed as one of the nation’s foremost freedom zones,” he said, noting that some New Yorkers moved to Florida during the pandemic. “We fought Trump’s own administration to make sure our kids could be in school and our businesses could be open.”
Mr DeSantis said that Mr Trump attacking him is a "huge mistake," and warned that he would be more pointed in his rebuttals to the former president going forward.
“Look, if someone is saying that, I’m gonna counterpunch and I’m gonna fight back on it,” Mr DeSantis told reporters in Iowa on Tuesday. “I’m going to focus my fire on Biden, and I think he should do the same. He gives Biden a free pass. I’m focusing on Biden. That’s my focus.”
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