Verstappen started the race at the Nürburgring third, and following a retirement for Valtteri Bottas after 18 laps, had dropped to 11 seconds behind Hamilton before a late safety car bunched the pack together.
On cold tyres, the Dutchman was unable to challenge Hamilton for the win, but did steal away the point for fastest lap with a last-lap effort.
"We finished second where I think we belong today and that's the most important thing," said Verstappen.
He added: "I think overall it was a good race. I was just trying to follow Lewis once Valtteri dropped out.
"I think the pace was good, we were just trying to do our own race. They were just a little bit too fast but the last few laps I just thought I'm going to give it a go and see what happens.
"We just managed to get that fastest lap but also that one extra point so I was pretty happy with that."
Both Hamilton and Verstappen felt the safety car remained on track for too long as the lapped cars were allowed to unlap themselves and rejoin the train before green flag racing resumed.
The possibility that the spectacle is being put ahead of safety was raised in Mugello, and it appears similar conversations may be held with race director Michael Masi between now and the Portuguese Grand Prix in two weeks.
Explaining the difficulties, Verstappen said, "The track is very cold and the tyres are already cold when you leave the box and I just didn't understand why the safety car was out for so long after the car was cleared.
"I understand they want to bunch up the field but it's pretty dangerous with these cars when the tyres are so cold."
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