The Briton, a five times winner in Shanghai, suffered a spin on cold tyres and ended the day some seven tenths of a second slower than the Finn.
"I'm just focusing on trying to figure out what the hell is going on with my car," the Formula One website quoted him as saying.
"I was struggling with the car today, so we've got work to do, particularly on my side as Valtteri looked much more comfortable in the car.
"We're going to work hard tonight to find some tweaks and hopefully come back stronger tomorrow; the car has the pace in it to compete at the front, we just need to find the right set-up."
Mercedes have finished the first two races of the season one-two, with Hamilton triumphant at the last round in Bahrain two weeks ago.
That was a lucky win, however, with the victory falling into his lap after Ferrari's Charles Leclerc suffered an engine problem with 10 laps remaining.
Bottas, winner in Australia, leads the championship by a point due to the extra point awarded for the fastest lap in Melbourne.
The Finn was fastest overall in Friday practice, with Hamilton fourth.
(Writing by Alan Baldwin in London, editing by Ken Ferris)
