The 30-year-old Englishman has only a 10-points advantage over the German following Rosberg's victory at the Austrian Grand Prix and knows he needs to regain his earlier supremacy to repeat his triumph in last year's race.
"I don't feel like I ever really reached my peak in Austria," said Hamilton.
"It wasn't the smoothest of weekends for me, so to come away with second place wasn't a disaster in the circumstances.
"It's something that will always stay with me and nothing less than the same again will do. I'm lucky enough to have fans all around the world, but winning in front of your home crowd is something else.
"We have a fantastic car this year, even better than in 2014 and it should suit this track. I'll be going all out to make the most of it."
"My week in Austria could not have come together much better," said Rosberg. "Apart from a mistake in qualifying, I felt right on top of things from the start and it was great to get another win.
"With the extra day in the car testing on Wednesday, also, helping the team prepare for Silverstone, I feel ready to go full attack at a circuit I really enjoy. It should suit our car nicely with the focus on down-force and we learned some useful things during the test.
