Hillary Clinton evinced ebullience with reporters on her plane the day after the first televised debate with Donald Trump, declaring he had made claims on stage that were “demonstrably untrue” and mocking him for suggesting he had somehow been given a wonky microphone.

She also seized on remarks by Rudy Giuliani, the former Mayor of New York, suggesting that Mr Trump might skip the two further debates that are scheduled before Election Day on 8 November unless he is given assurances the moderators at each of them will treat him better.

“If I'm the only person onstage, well, you know, I'm the only person onstage,” Ms Clinton said, clearly savouring the mostly kind reviews of her performance at Hofstra University on Long Island on Monday night and the rather less glowing assessments of his.

Mr Trump’s response on Tuesday appeared to be first to blame everyone but himself if the perception was that he had fallen short at the debate and to attempt belatedly to deflect some of the more effective attacks that Ms Clinton had unleashed against him, thus making sure the media spotlight stayed on them when it was perhaps in his best interests that it did not.

US election 2016: the race for the White House in pictures Show all 12 1 /12 US election 2016: the race for the White House in pictures US election 2016: the race for the White House in pictures Republican U.S. presidential nominee Donald Trump shakes hands with Democratic U.S. presidential nominee Hillary Clinton at the conclusion of their first presidential debate at Hofstra University in Hempstead, New York Reuters US election 2016: the race for the White House in pictures President Barack Obama embraces Democratic nominee Hillary Clinton on stage at the party's convention in Philadelphia US election 2016: the race for the White House in pictures Donald Trump's wife Melania delivered a speech at the GOP convention in Cleveland that was later found to have been cribbed in part from Michelle Obama's 2008 convention address AP US election 2016: the race for the White House in pictures Hillary Clinton talks to reporters aboard her new campaign plane on Labour Day, 5 September, her first 'press conference' since 2015 (Getty Images) US election 2016: the race for the White House in pictures Donald Trump held a joint press conference with Mexican leader Enrique Pena Nieto in Mexico City in August, hours before reiterating his harsh immigration plans at a campaign rally in Arizona Reuters US election 2016: the race for the White House in pictures Bernie Sanders officially endorsed Hillary Clinton, saying his progressive vision for ‘a transformed America’ would be ’best served by the defeat of Donald Trump’ Reuters US election 2016: the race for the White House in pictures Khizr and Gazala Khan appeared at the DNC to slam Trump for his stance on Muslim immigration, citing the case of their son Humayun Khan, who was killed in combat while serving as a Captain in the US Army in Iraq US election 2016: the race for the White House in pictures Libertarian candidate Gary Johnson is doing better in polls than any third party candidate since Ross Perot, 20 years ago Nicholas Kamm/AFP/Getty US election 2016: the race for the White House in pictures Green Party candidate Jill Stein (centre) marches with supporters in Colorado AP US election 2016: the race for the White House in pictures Hillary Clinton and Virginia Senator Tim Kaine at a rally in Kaine's home state in July, days before Ms Clinton tapped him to be her running mate Getty US election 2016: the race for the White House in pictures Trump on the campaign trail with his vice presidential pick, Indiana governor Mike Pence AP US election 2016: the race for the White House in pictures Former Ukip leader Nigel Farage appears at a Trump rally in Mississippi in August, where he told the crowd that he 'wouldn't vote for Hillary Clinton if you paid me'.

That included his returning to an allegation that he had shamed a winner of a beauty pageant he once owned calling her “Miss Housekeeping”, apparently because she was from Latin America. On Tuesday, he implied she deserved his scorn because she gained weight. “She gained a massive amount of weight. It was a real problem. We had a real problem,” he told Fox News.

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Arguably, Mr Trump had opened himself up to additional post-debate mockery with his suggestion that debate organisers may have given him a microphone that was faulty or set at a lower volume than Ms Clinton's. “My mic was defective within the room,” Mr Trump told reporters before leaving the venue on Monday. ”I wonder … Was that on purpose? Was that on purpose?”

“Anybody who complains about the microphone is not having a good night,” Ms Clinton suggested to reporters on her plane on Tuesday just before returning to her seat for a flight to North Carolina where she was due to hold her first post-debate rally.

She also sought to contrast how she sees America with the more dystopian characterisation of it that Mr Trump offered on Monday. He had spoken of the country in “dire and dark terms”, she said, adding: ”That's not who America is.“

Clearly aware that she was having a better ‘day-after’ than her rival, Ms Clinton said she had had a “great, great time” and was “thrilled” with how it turned out. There had been widespread agreement among political commentators on Tuesday morning that she had come far more prepared for the debate than he had even if some thought she had occasionally seemed smug.

She also sought briefly to reiterate the contention she had made on stage that Mr Trump lives in his “own reality” when it comes to some of the things he said. She agreed that he “was making charges and claims that were demonstrably untrue, offering opinions that I think a lot of people would find offensive and off-putting.”

Also on the trail yesterday, Vice President Joe Biden excoriated the Republican nominee for responding to Ms Clinton’s assertion that he had avoided paying income tax to the federal government for years by calling himself “smart” for it. “What in the hell he is talking about?” Mr Biden said, campaigning for Ms Clinton in Pennsylvania.

Xavier Becerra, a Congressman from California who is the chairman of the Democratic Caucus in the House of Representatives, told reporters that Mr Trump had seemed to come “unhinged” at moments in the debate, although he didn’t specify which ones they were.