A day after claiming her party’s nomination for president, an exhilarated Hillary Clinton said she was “still processing” the emotions of the moment on Wednesday as she heard from people around the globe both excited about her success and deeply anxious about her Republican rival, Donald J. Trump.

In a brief but at times introspective interview, Mrs. Clinton said that although other countries have been led by women, such a milestone would be different were it to happen in the United States. She called the demands of the American political system more personally grueling and difficult.

“I really believe our system is probably the most challenging in the world,” Mrs. Clinton said. “If you’re a prime minister, you’re chosen by your peers,” she continued. “If you’re president, you run statewide, but it’s usually with the backing of a party and you don’t have to raise the money to run.”

But, she added, “Women candidates all face the same scrutiny, and questions about ourselves, so there are similarities.”