Hamilton has suffered a string of engine problems that have affected his title hopes this season and seen Mercedes team-mate Nico Rosberg establish a substantial lead.
Hamilton said: "I was just petrified the car wasn't going to make it.
"That's probably the first time in my whole career I have had that weighing heavily on my heart throughout the whole thing."
Hamilton said that when he finally crossed the line to take his first win since the German Grand Prix at the end of July it was "a release".
"It was the longest afternoon I had probably in my whole career, just hoping the car makes it to the end. "Every single lap I was thinking something might happen."
Hamilton said he was "haunted" by what had happened to him at the Malaysian Grand Prix two races ago, where he dominated only for an engine problem to take away a victory that would have given him the championship lead.
Instead, he came away from that race with a 23-point deficit to Rosberg, which extended to 33 when Rosberg won the following weekend in Japan while Hamilton finished third.
Media playback is not supported on this device
The gap is now 26 points after Rosberg finished second to Hamilton in Austin.
Rosberg can still finish second to Hamilton at all three remaining races and win the title.
Hamilton said: "I just want to keep my head down and do the best job possible all weekend and I can't control what will happen behind. All I can do is make sure when I leave this season I know I did everything with a full heart."
Hamilton's win was the 50th of his career - he is only the third driver to reach that landmark after Michael Schumacher and Alain Prost.
And he is now only one win short of the Frenchman's tally of 51 grand prix victories. Schumacher is way ahead on 91.
Hamilton said: "I had completely forgotten it was going to be the 50th. It's been a long time coming.
"I know I've mentioned it before, but I have been here for 10 years, I've had lots of ups and down and lots of great opportunities to work with some incredibly gifted people who have helped me get here today. Then my family as well without whom I wouldn't be here today.
"It's kind of very surreal, for sure. I can't believe there are only three of us but hopefully on to bigger and better things."
Lewis Hamilton says he was "petrified" during the United States Grand Prix that a reliability problem would cost him another win.