Fernando Alonso said his first podium of the season was the result of car improvements and his own performance.
He dedicated his third place in China to former boss Stefano Domenicali, who resigned after Ferrari drivers were ninth and 10th in the last race.
Alonso said the car felt "more competitive" thanks to "new parts".
"On the personal side I had a fantastic weekend, probably at the level of 2012 in terms of driving and feeling comfortable," he added.
"Hopefully we can give some great Sundays at home in front of the TV to Stefano."
Alonso's 2012 remark is a reference the season regarded as the two-time champion's finest.
In 2012, he took what was acknowledged to be the fourth or fifth fastest car to the brink of the world championship, narrowly losing out to Red Bull's Sebastian Vettel at the final race.
"We were a minute behind the leaders in Bahrain, ninth and 10th and today we were seven seconds behind Rosberg which is good," Alonso said.
Team-mate Kimi Raikkonen finished eighth, more than one minute behind Mercedes.
"We need to keep working and have the two Ferrari's on the podium and hopefully at the next one we'll be a little bit closer to that target, Alonso said.
Domenicali's resignation came after Ferrari president Luca Di Montezemolo, who was in Bahrain, made clear his disappointment at Ferrari's performance there.
His replacement, former head of Ferrari's North American road-car division Marco Mattiacci, was attending his first grand prix in his new role in Shanghai.
Alonso said: "Stefano felt probably not happy with his job or his life at this moment so he decided to step back.
"Obviously this podium is dedicated to him in a way because probably all the parts from now until July or August are coming from the team working under Stefano."
He said he was encouraged by Ferrari's step forward in form but said they still had a long way to go to catch the dominant Mercedes cars.
"Mercedes looked very dominant again," he said. "It is not enough. We need to catch them as soon as possible before the championship is over.
"Barcelona will be a Red Bull track, with not many straights so they can exploit the potential they have with aerodynamics so it's going to be a tough weekend."