File Photo: Mercedes British driver Lewis Hamilton. AFP
The seven-time champion Mercedes driver said he had hoped to fight for a front row start in Sunday's race, but was unable to find the pace required in the final minutes of a sodden rain-lashed session.
He admitted he was disappointed, but said he felt equally sad to learn that the 27-year-old Dutchman was booed after qualifying second behind maiden pole-sitter Carlos Sainz of Ferrari.
Verstappen beat him to the drivers' title last year after an acrimonious season, including a high-speed crash at Silverstone where the 37-year-old Briton won after his rival was taken to hospital.
"I think we're better than that, so I would say we don't need to do booing," said Hamilton. "But we've such great fans and our sporting fans, they feel emotion up and down.
"I definitely don't agree with booing. We don't need to do that. We should be here pushing everybody.
"It doesn't make a difference when you boo someone. They've already made the mistake or whatever it is, but I really do appreciate the support I have here -- and maybe some of them are still feeling the pain from last year so, either way, I appreciate it."
A crowd of more than 130,000 braved the cold and wet weather for qualifying and many appeared to enjoy Verstappen making a mistake in Q3 that cost him pole position and booed him when he was interviewed in the pit lane after the session.
Verstappen shrugged off the abuse, saying: "It was a bit disappointing because I couldn't really understand Billy (the post-session interviewer) and it was a bit of a problem.
"But, the rest … if they want to boo, they can do that. For me it's not going to change anything. I'm always happy to be here. It's a great track.
"It's a great atmosphere in general. Maybe some of them, they don’t like me, but that's fine. They all have their own opinions, you know?”
Hamilton remained optimistic that he can bid for an unprecedented record ninth win at a single Grand Prix venue.
"It makes it a little harder tomorrow, but we've got a good race car and we'll continue working," said Hamilton.
"We brought some parts for the car, but it wasn't necessarily a big upgrade," he added. “But it was definitely an improvement and we seemed to have closed up a little bit. I think in the dry we wouldn't have been able to compete for top three or anything like that.
"Fifth is going to be tough, but I'm going to try and work my way forwards.
"I'm a little bit gutted, really, because obviously we have such a great crowd here, but I will definitely be aggressive tomorrow -- don't worry!"
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