Hamilton lost the lead to eventual winner Fernando Alonso's Ferrari on the fifth lap, and then spent the afternoon in a battle with Kimi Raikkonen's Lotus, which he ultimately narrowly lost.
"I am not really sure where we are losing out," Hamilton admitted.
"Today just the overall pace was not there and there are definitely a couple of areas we can focus on on the car.
"We have some updates and need to keep improving. We have to work out where we are losing the time, try and zone in on that and improve that."
But he underlined that he was still satisfied to get on the podium for a second straight race, even if Alonso and Raikkonen were quicker.
"I am quite happy with third, though I would have loved to win," said Hamilton.
"They were a little bit too fast for us during the race. I was able to apply a little bit of pressure to Kimi but not overtake."
Hamilton's team-mate Nico Rosberg, who won in China a year ago, retired early with a suspected suspension issue.
"I had a lot of understeer, then after the pitstop it got worse and my front wheel started bouncing on the inside of the corners," Rosberg said.
"I came in to check the car but it stayed like that so I retired."
- Sports & Recreation
- Kimi Raikkonen
- Fernando Alonso