Mr Trump said he held back “because he didn’t want to hurt anyone’s feelings”.
In a Fox News interview, he also accused moderator Lester Holt of being tougher on him than on Mrs Clinton.
Overnight polls with small samples were split on who won, but more rigorous surveys are due in the coming days.
Asked how he felt about the debate on the television news programme Fox and Friends on Tuesday, Mr Trump said it had gone well, but complained that Mr Holt had not pressed Mrs Clinton on her “scandals”.
“He didn’t ask her about the emails, he didn’t ask her about the scandals, he didn’t ask her about the Benghazi deal. He didn’t ask her about a lot of things he should have asked her about. Why? I don’t know,” he said.
He said he felt tempted to bring up “the many affairs that Bill Clinton had”, but held back because the Clintons’ daughter Chelsea was in the audience.
“I may hit her harder in certain ways. I really eased up because I didn’t want to hurt anybody’s feelings,” he added.
Asked whether Hillary Clinton had got under his skin, Mr Trump said “at the end maybe, at the very last question”.
Mrs Clinton had brought up the case of Alicia Machado, a former Miss Universe, saying Mr Trump called her “Miss Piggy” after she gained weight.
But Mr Trump brushed away her accusation said Ms Machado had “gained a massive amount of weight” making it a problem for the Miss Universe pageants, of which he was the owner.
After the debate, Mrs Clinton posted a campaign video in which Ms Machado describes how she had been treated by Mr Trump.
Mr Trump also said his microphone was “terrible” and crackled, and that his volume was lower than Hillary Clinton’s microphone. He blamed this for what some listeners thought were sniffles by Mr Trump during the debate.