Verstappen, 25, last month clinched his second successive crown with four races to spare.
The Dutch driver and Hamilton battled until the last lap of the final race in 2021 in Abu Dhabi, with Verstappen prevailing after former race director Michael Masi made a controversial change to the safety car re-start procedure.
This year, Red Bull have far outperformed Hamilton's Mercedes team and Verstappen has won a record 14 races out of 20 with two remaining.
"I think he's done an amazing job, he's done everything he had to do. The team provided him with an amazing car and he's delivered pretty much every weekend," Hamilton told reporters at the Sao Paulo Grand Prix on Thursday.
"He can be proud of the job he's done, I know what it feels to be in a position like that," added the 37-year-old Briton, who has yet to win this year.
Red Bull have also clinched the constructors' world title for the first time since 2013 after eight championships in a row for Mercedes, who are 40 points behind second-placed Ferrari.
Hamilton said securing the runner-up slot was important for team staff as it meant higher bonuses at a time when Britain was going through a cost of living crisis with energy costs rocketing.
"I'm told and I can see how impactful and important that is for them," he said.
Hamilton was this week made an honorary citizen of Brazil by the country's lower house of Congress and has visited a slum in Rio de Janeiro where he met with children from a social project.
The Briton, who last week attended an event to promote next year's inaugural Las Vegas Grand Prix, said he was more excited to be in Brazil than Nevada.
Hamilton has won three times at Sao Paulo's Interlagos circuit, where he was also crowned world champion for the first time in 2008.