NEW YORK - Fresh off their first presidential debate, Hillary Clinton and Donald Trump were back on the campaign trail Tuesday.

Clinton spoke to reporters aboard her plane earlier in the morning and says she thought she did well in the debate. The Democratic nominee also says she is looking forward to the next one on October 9.

Clinton says Trump once again showed that he lacks the right demeanor for the White House.  

"I thought on several occasions he was making charges and claims that were demonstrably untrue. Offering opinions that I think a lot of people find offensive and off-putting. He can run his campaign and present himself however he chooses, but the real point is about temperament and fitness and qualification," Clinton said.

Meanwhile, calling in to "Fox and Friends" Tuesday morning, Trump claims he was asked tougher questions, but says he still performed well despite the disadvantage.  

"They were leaving all her little goodies out, they didn’t ask her about much. I was asked about my tax returns, which I’ve told about 500 times. I think I really did well when we were asked normal questions, I did really well in answering those questions. But those questions are not answerable in a positive light," said Trump.

Clinton has a rally scheduled in North Carolina, while Trump will be stumping in Florida.

The two presidential candidates met for their first debate Monday night in a more than 90-minute matchup that has left many New Yorkers talking and weighing in on who won.

• See our complete TWC News/NY1 blog of the event.

The event at Hofstra University, in front of a largely New York audience, was moderated by NBC Nightly News anchor Lester Holt.

On the topic of fighting crime, Trump said it was imperative to bring down the crime rate in big cities like New York and Chicago.

"Almost 4,000 people have been killed in Chicago since Barack Obama became president.  We have to bring back law and order," Trump said.  "Stop-and-frisk worked very well in New York -- Mayor Rudy Giuliani is here -- it brought the crime rate way down."

"The argument is that it's racial profiling," Holt said of the controversial practice that was the subject of a federal lawsuit againt the NPYD in 2013.

"No, the argument is that we have to take the guns away from these bad people who shouldn't have them," Trump responded.

Clinton, in her retort, said that she respected the work of the NYPD in reducing New York City crime to record low levels.

"But too many African American and Latino men have ended up in jail for non-violent offenses," Clinton said.  "It's just a fact that if you're a young African American man, and you do the same thing as a young white man, you are more likely to be incarcerated.  We've got to address the systemic racism in our criminal justice system."

The discussion led to a larger back-and-forth on the topic of race. 

"The African American community has been let down by our politicians," Trump said.  "They talk good around election time, like right now, and after the election they say 'See you later, I'll see you in four years.'"

"I think that Donald just accused me of preparing for this debate -- and yes, I did," Clinton said.  "And you know what else I've prepared for?  I've prepared to be president.  And I think that's a good thing."

In a separate exchange, Clinton pushed Trump to release his tax returns, which the real estate mogul said he would do it if she would produce the more than 30,000 e-mails that her staffers deleted from her personal e-mail server when she was secretary of state.

Clinton, acknowledging that her use of the server was a mistake, said, "If I had to do it over again, I would obviously do it differently."

In another clash, Trump was asked about comments he had made that Clinton doesn't have the look of a president.

"She doesn't have the look, she doesn't have the stamina," Trump said.  "You have so may different things you have to be able to do as president, and I don't think she has the stamina."

"As soon as he travels to 112 countries...or even spends 11 hours testifying in front of a Congressional committee...he can talk to me about stamina," Clinton retorted.

"I agree, Hillary has experience," Trump said, "but it's bad experience."

Also in dispute during the debate: Clinton's government-driven approach to growing the economy versus Trump's tax-cut approach.

"You have what is called now the Trump loophole, because it would so advantage you and business you do," Clinton said to the billionaire during an early clash.  "It's Trumped-up trickle down.  Trickle down didn't work -- it got us into the mess we wee in in 2008 and 2009.  Broad-based, inclusive growth is what we need in this country, not more advantages for people at the very top."

"Typical politician.  All talk, no action." Trump replied.  "Our country is suffering because people like Secretary Clinton have made such bad decisions.  We are in a big fat ugly bubble right now, and we better be awfully careful."

The debate got off to a civil start, albeit briefly, as both candidates addressed questions about how to secure American jobs. 

"Donald, it's good to be with you," Clinton said to Trump at the end of her answer, in which she discussed investing in infrastructure and pursuing equal pay for women.

Trump, in response, called for a tax on companies that move manufacturing overseas.

"If you think you're going to make your air conditioners or your cars, and bring them into the country without a tax, you're wrong," he said.

"Under his tax plan, which would blow up the debt, we would lose three and a half million jobs," Clinton retorted.

The debate was divided into six segments of 15 minutes each, the first two of which focused on "America's direction," with the next two dealing with the economy and the final two focusing on national security and foreign policy.

Some experts were predicting the debate would draw more than 100 million viewers overall, which would break the current record of about 80 million viewers, set in 1980 in the debate between Ronald Reagan and President Jimmy Carter.