The Brit is 22 points behind drivers' championship leader and Mercedes team-mate Nico Rosberg in what has been an enthralling battle that has six rounds to play out.
Hamilton was victorious in Italy and carries that confidence into Sunday's Singapore Grand Prix.
The 2008 world champion said he was happy to still be in the hunt after an unlucky season, which has included three retirements.
"Obviously, with Nico coming second [at Monza] I haven't been able to close the gap too much - but there's still plenty of points to be won and I'm glad to have taken a step forwards," Hamilton said.
"Despite the highs and lows, I'm still well and truly in the hunt for the championship and that is something that gives me huge motivation for the final six races - starting in Singapore."
Hamilton won in Singapore in 2009, and that result is mixed with a third in 2008, two retirements and a pair of fifth-placed finishes at the race.
He is hoping his luck changes at the Marina Bay Street Circuit.
"It's a great place to begin the final flyaway phase of the season. The city is buzzing and the track is mega. It's a street circuit and I love street circuits," Hamilton said.
"I won there in 2009 which was a really special experience, plus I had a podium - which should really have been a win - at the first race in 2008.
"My luck hasn't been great at this circuit since then but hopefully that will change."