Most of the drivers took the opportunity to test out the conditions on intermediate tyres as rain fell during the final hour of practice in Barcelona on Saturday morning.
But Hamilton decided against running on the wet-weather tyres, something that Rosberg - who pipped the seven-time world champion to the world title in 2016 before retiring from F1 - questioned.
"Look, now Lewis is in a rush to get his belts on because he was out of the car,” Rosberg said during Sky’s coverage.
"I think Bradley [Lord, Mercedes communications director] should have had a word with him.
"Maybe this is Bradley, that's why Lewis is back in the car.”
Having revealed he had spoken to Mercedes after the session, Rosberg added: “Lewis could have perhaps made a little bit of a better effort in FP3 and been out there more to learn a bit more.
“It was in fact his decision to be in the garage for all that time and to also go out a bit late on the softs. So they [Mercedes] did say it was perhaps not 100 percent ideal.
“But then again, as a seven-time world champion you could allow yourself to do that.”
Hamilton showed potential signs of improvement for Mercedes after a difficult opening day of practice by ending FP3 third behind the two Red Bulls.
The Briton, who admitted at the end of Friday that he feared for his top-10 chances in qualifying, was just over four-tenths shy of Max Verstappen’s benchmark.