The Briton took his first pole position since joining Mercedes in China last weekend and a third-placed finish means he is just 12 points adrift of points leader Sebastian Vettel.
And although Mercedes did not have the race pace to match Fernando Alonso's dominant Ferrari, Hamilton feels the team is on the path needed for the campaign ahead.
When asked if he felt after a back-to-back podiums that he was in a title fight, Hamilton said: "I am. I definitely feel like that at the moment.
"But, I am not focusing on the title because you never know.
"Look at Nico Rosberg's car today [which retired with anti roll-bar failure]. It didn't finish and that could happen to me any time, although fingers crossed it does not.
"It can happen to anyone. Fernando didn't finish the last race and he is scoring high points, so he is looking very strong."
Hamilton reckons his Chinese GP race performance had been compromised by balance issues caused by rubber debris getting caught in his front wing, although he does not believe the team had the speed to beat Alonso even without the problems.
"I don't feel we were harder on the tyres, we just generally didn't have the same pure pace," he said.
"In terms of looking after the tyres, we had a couple of problems with the front wing.
"We were losing downforce, so the balance was shifting quite a lot from understeer to balanced, and then balanced to understeer. So we need to fix that."
Hamilton said that the amount of progress that Mercedes has made since last year was ultimately proved by there being a feeling of slight disappointment at 'only' finishing third.
"We are really happy with it, and it is almost to the point that it shows how we have improved so much," he said.
"To be disappointed with a third is a fortunate position to be in.
"It has been a good weekend. Of course I would have loved to have won, as that is what I came here to do, but we just were not as quick as the Ferraris.
"Maybe if we did not have some of the issues with the front wing then I might have been able to overtake the Lotus [of Kimi Raikkonen], maybe, but they were still very quick even though he had problems with his front wing.
"We just need to improve. As Ross [Brawn] said on the radio, we are not quite there yet but we are not that far away."