Victory in Monaco was his first in seven months and cut Mercedes team-mate Nico Rosberg's title lead to 24 points.
"I've proven that I'm just as strong as I've ever been and I will be for the rest of the year," said Hamilton.
"There's a long way to go yet, though. We've seen from the first six races that anything's possible."
Rosberg won the first four races as Hamilton's title defence started with a series of problems, errors and technical failures.
But the Englishman said he was optimistic of a strong showing at this weekend's Canadian Grand Prix, the track where he took the first of his 44 grand prix victories back in 2007.
"Montreal has always been a good track for me, so hopefully I'm able to shine like I did the first time I went there in that great city atmosphere," he said.
Rosberg had a poor race in Monaco, lapping well off the pace in the early stages before being ordered to let Hamilton by so the Briton could compete for the win with Red Bull's Daniel Ricciardo.
As the race went on, he slipped further down the field and was passed on the run to the line by Force India's Nico Hulkenberg to finish seventh.
"I expected and prepared myself for some difficult races after the awesome start to the season," said the German.
"In the last grand prix, I hopefully got all of my bad luck out of the way in one race, so onwards and upwards again from now."
Defending champion Lewis Hamilton says his first win of 2016 is evidence that he is as good as ever following a difficult start to the season.