Mrs. Clinton succeeded several times in baiting Mr. Trump, making him become defensive, lose his cool or dig himself into a political hole, particularly late in the debate as he struggled to defend himself against charges that he had made sexist and racist remarks. He also repeatedly interrupted or talked over Mrs. Clinton, which some female voters found alienating. Some allies of Mr. Trump say he is not preparing enough to do battle with a woman in mind; he has only one senior adviser who is a woman, his campaign manager, Kellyanne Conway.

Almost all of his advisers rejected the idea that the debate was a failure for Mr. Trump, noting that he landed some punches and insisting that Mrs. Clinton looked more polished than she was because of her opposition.

But all of them described the debate as filled with missed opportunities. And they openly expressed frustration that Mr. Trump seemed unable to stop chasing chum that Mrs. Clinton tossed at him.