Top seed Sinner, the first Italian man to reach a US Open singles final, received medical attention beside the court during the gruelling straight-set win, while his opponent vomited three times in the New York heat.
"The physio (loosened) it up very fast on court, so after I felt OK in the beginning. Then, after, it went away by playing, which is good," Sinner told reporters.
"Let's see how it is tomorrow when it's cold. It's going to be a different feeling. Hopefully it's nothing to concern about."
Sinner said he expected Britain's Draper, who reached a Grand Slam semi-final for the first time, to be a strong contender.
"Playing against Jack, it's never easy. He served very well... Happy to win this one," Sinner said. "I know that he's potentially winning some big titles in the future."
The Australian Open champion, who faces American 12th seed Taylor Fritz in the final on Sunday, said he expected a difficult match, playing against a home favourite hoping to end the host nation's 21-year men's Grand Slam drought.
"Big serve. Very solid player from the back of the court. He can hit strong. He can hit with rotation. He can mix up the game very well," Sinner said.
"We're in New York playing against an American, so it's going to be, for sure, the crowd a little bit more on their side. But it's normal. It's like when I play in Italy... so I'm going to accept that."
