Hamilton, who started third on the grid, was closing in on Verstappen in the final laps but in the end crossed the finish line two seconds behind the Dutchman, who claimed his 15th win of the season.
Mercedes executed a slightly different two-stop strategy and, as Hamilton acknowledged afterwards, in hindsight should have pitted the seven-time world champion earlier in the first half of the race.
“We should’ve stopped before Lando [Norris],” said Hamilton.
“I don’t know why we didn’t… the deficit was so hard. We’ve got some work to do.”
Mercedes came to Austin with an upgraded floor and it seemed to improve performance, with Hamilton satisfied with the team’s latest step despite the near-miss.
However, the seven-time world champion added that the pit stops weren’t quite top-notch in Texas.
“Other than that, it’s a step forwards,” he continued. “We need to pick up on some areas, the pit stops and strategy maybe, but it’s right there.
“Verstappen started sixth and he was out in front. They [Red Bull] are still ahead and they’re not developing now – they’re just chilling.
“We’ve got a huge amount of work to do.”
It is the closest Hamilton has come to winning a race this season. The 38-year-old still hasn’t won a race since December 2021 in Saudi Arabia, but is now closing in on Sergio Perez for second place in the world championship.