The Mexican has been suffering a run of poor form as he battles to finish second overall in a championship already won by Verstappen.
Hamilton is Perez's closest rival for the runner-up slot but is now 39 points behind with four rounds remaining after failing to score in his last two races.
"I don't think his team has been really massively supportive," Mercedes' seven-time world champion Hamilton told Fox Sports television.
"Not all his team, because there's a lot of people on a team, but a couple - one of them particularly, a spokesperson, has not been really great, not helping psychologically.
"If I heard (Mercedes boss) Toto (Wolff) talking negatively about me over the weekend that would've been really tough, so it's a difficult environment for him (Perez), but I think he has dealt with it to the best of his ability."
Hamilton did not name any individual but Red Bull motorsport consultant Helmut Marko, a prominent figure in the team's leadership, was given a written warning by the governing FIA in September for comments he made about Perez.
The 80-year-old Austrian had blamed Perez's patchy form on his ethnicity and also referred to him as a South American.
Perez started the season by taking the fight to Verstappen, each driver winning two races in the first four, but his challenge then collapsed and the Dutch driver ran away with 10 wins in a row.
Red Bull team boss Christian Horner has hinted at a confidence crisis, saying this month that Perez had got into a "spiral mentality".
"We can't afford to have a big split (in performance between the pair) because if the grid continues to concertina next year, we need both drivers delivering at the top of their game," he warned then.
Speaking on Friday, Horner said Perez had been working hard behind the scenes with his engineers to get himself "on the front foot in these remaining races.
"He had a strong start today and a good race just a week ago in Austin and hopefully he can build on that confidence and that performance."
Horner was also quick to shoot down any talk of rivalry between his drivers.
"There is no rivalry between the two drivers. They actually get on very well, they've got on very well for three years," he said.
"Whilst I'm sure the media would love them to be at each others' throats, unfortunately for you guys they aren't. They work very well together off track and on track as we've seen on many occasions."
