Verstappen starts third for the race at Silverstone, albeit finishing a second adrift of polesitter Hamilton who set a new lap record of one minute 24.303secs.
Although Verstappen expressed concern over the gap to Mercedes he does not believe his weekend is over.
"In the race it's different," said Verstappen. "I believe we are a little bit closer in the race. I don't say that I'm going to fight them but at least we have a fighting chance starting third."
Assessing his qualifying performance, Verstappen added: "I think the lap at the end of Q2 was pretty good, but you could see very early on in qualifying they [Mercedes] were just way too fast, like they have been the last few races.
"You just have to accept that. You try to do the best you can and that's P3 for us, so I'm pretty pleased about that."
Red Bull has suffered at recent grands prix with moments of snap oversteer, and a crash during practice for Verstappen's team-mate Alex Albon, who starts 12th, further highlighted the problem.
Verstappen explained: "With these new types of cars from the last few years, they're very sensitive to wind because they're that big and that wide, and especially here at Silverstone you can really feel that.
"Yesterday, for example, it was really tricky in the low-speed corners. Today, the wind changes and it becomes like a completely different car, luckily in the right way, because today was a lot more fun to drive."
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