But columnists also noted that Republican Mr Trump had the ability to "adapt after failure" and said there was a risk Mrs Clinton could become "cocky" after her assured performance.
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New York Times
The editorial board was unimpressed with the debate, saying "when just one candidate is serious and the other is a vacuous bully, the term loses all meaning".
Opinion writer Nick Kristof said Trump had "hurt himself", others said Mrs Clinton had "crushed" her opponent.
But Ross Douthat said Mrs Clinton did not "goad Trump into a true meltdown or knock him out with a truly devastating attack". She "won the night, but he lived to fight another day", he said.
Washington Post
Writers unanimously called it for Mrs Clinton, saying Mr Trump had "bombed on the ultimate reality show" and "did not appear ready to be president".
Stephen Stromberg mused on what a debate victory for Mrs Clinton actually meant.
"If Americans were so evenly split heading into Monday night, after the monstrous campaign Trump had run before the debate, they may be capable of anything," he wrote.
Fox News
Pundits consulted by the broadcaster said Mr Trump had "struggled", "never took control" and "failed to exploit" the issue around Mrs Clinton's emails.
"It helps to be prepared," said Douglas Schoen, declaring victory for Mrs Clinton.
"On so many fronts he should have been able to wipe that smug grin off Hillary's face; he did not rise to the challenge," said Liz Peek.
LA Times
Its panel of three commentators had Mrs Clinton winning every round.
"Politics is harder than it seems, and Trump found that out tonight," said Cathleen Decker. "Clinton was unflappable... and probably likeable enough," said Doyle McManus.
David Lauter said Mr Trump's lack of preparation echoed the "terrible job" President Obama did in the first TV debate four years ago. "But remember that Obama bounced back," he said.
Breitbart
Writers at the hard-right news website said Mr Trump had "bludgeoned" Mrs Clinton on trade.
They also accused debate moderator Lester Holt of "shilling" for Mrs Clinton by asking Mr Trump "tough questions" and insisted that Republican candidates were "routinely treated unfairly" by moderators.
Some 75% of Breitbart readers said Mr Trump had won.
The Hill
Republican and Democrat-supporting pundits consulted by the Washington politics website mostly said Mrs Clinton won, but in a poll its readers called it for Mr Trump.
Hillary "looked confident, calm and composed, while Trump appeared frantic, nervous and distracted", said former Republican congressman John LeBoutillier.
But former Republican campaign aide Ford O'Connell declared a draw, saying going "toe-to-toe" with Mrs Clinton on the debate stage "elevated Trump's legitimacy as a candidate".
NY Daily News
The tabloid's verdict: "A grumpy loser! Trump pesters, interrupts Hillary throughout debate - but Clinton gets the last laugh."
Russia
Commentators at the independent Nesavisimaya Gazeta newspaper said Mr Trump appealed to Russian sympathisers in the US, who "like his proposal to restrict the access of illegal migrants to the country" and his lack of the "political correctness of which we are sick and tired".
The debate is trending on Twitter in Russia, where some pro-Kremlin bloggers are hailing Mr Trump's performance.
The Arab world
Saudi-funded al-Arabiya focused on "heated arguments" over the economy and unemployment.
Qatar's al-Jazeera's Washington correspondent said Mr Trump had tried to "hold Clinton responsible for the failure of [US] Middle Eastern policies" and causing "chaos in the region".
Iran
The IRINN rolling news channel highlighted Mrs Clinton's remark that US sanctions "brought Iran to the negotiation table" in the lead up to the nuclear deal.
It also focused on Mr Trump's denunciation of the deal as "one of the worst historical deals done between two countries".
Who do world media think won US debate?
The US media have given their verdict on who won the first debate - with most awarding victory to Democratic candidate Hillary Clinton.