The German was forced to make four pit stops on the way to his ninth-placed finish at the Bahrain Grand Prix, when most leading drivers only made three.
The Silver Arrows have suffered issues with rear tyre usage since 2010, and Rosberg says that finding the solution will not be easy.
"The great thing is we have a great car," Rosberg told BBC Sport.
"We just need to sort out these tyre issues, which is easier said than done.
"It is a massive mission and it is the same for everyone. Some people are doing a better job so we are pushing hard for that."
Rosberg had qualified on pole for Sunday's race, but failed to hold onto the advantage.