Vettel has struggled in his Ferrari this season, failing to finish on the podium in each of opening two races.
The German has come under increasing pressure as the Prancing Horse struggle to end a 12-year Championship drought.
Ferrari were tipped to leapfrog Mercedes as the favourite team for silverware this season but so far that has failed to materialise.
It means many pundits and fans have backtracked on their early-season predictions already.
However, Mercedes star Hamilton backed his German rival to get out of his current rut.
And Vettel was surprised by the support he received from such a fierce rival.
“I didn’t know he had said anything nice but it’s nice to hear,” Vettel said in Shanghai.
“Maybe he’s the only one that doesn’t lack a short-term memory.
“We’ve been around a long time and as much as I want to beat Lewis, he wants to beat me but sometimes you never know what exactly is going on with other people in other teams.”
Vettel blamed his car for his poor start to the season.
“I wasn’t happy with my performance [in Bahrain], not happy with the feeling yet with the car, the feeling that I had prior to the season in testing,” Vettel added.
“I know I can do better and I know we have lots of races to show and prove that.”
However, the four-time world champion hopes the testing which took place in Bahrain last week will help him out.
“It’s normal that you never get the car that you want so you always have to adapt,” Vettel said.
“Very rarely you get races where the car is absolutely fine and you have nothing to complain about.
“I think the [in-season] test was very helpful and useful to get some laps in the car and I think we learnt some things about the car, car behaviour that maybe we couldn’t in Barcelona because we were looking at other things.
“The behaviour in Barcelona was very strong so hopefully I have a better feeling in the car this weekend.”