Hamilton made the better launch to take the initiative into the first corner, only for an aggressive strategy from Red Bull to allow Verstappen to perform what was ultimately a race-winning undercut.
Hamilton did cut a near nine-second gap to the Dutchman to just one by the end of the race but wasn't able to reach the all-important DRS activation range, with Verstappen hanging on to stretch his lead to 12 points at the top of the standings.
"Firstly, congratulations to Max, he did a great job today," said Hamilton.
"It was such a tough race. We got a good start and gave it absolutely everything but at the end of the day, they just had the upper hand and we couldn't have really asked for more.
"Big thanks to my team for great pit stops, great hard work throughout the weekend."
A weekend attendance of 400,000 fans watched events unfold at the Circuit of the Americas showing further proof of F1's growing profile in the United States.
Hamilton added: "I think this is definitely our acceptance into the US. What a place to be.
"It is a real honour to be out here. I hope we have more races out here and I hope the sport continues to grow because you can tell just how great the fans are out here so I hope we get to come out more."
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