Mercedes is being hauled before the FIA tribunal to face possible sanctions for breaching the rules about in-season testing, after running its 2013 car during a test with Pirelli recently at Barcelona.
World champion Vettel, whose Red Bull team lodged the original protest together with Ferrari, said Mercedes obviously got an unfair advantage.
"I see it as a critical issue," he told Suddeutsche Zeitung newspaper.
"Each test kilometer is an advantage, and Mercedes had the opportunity to test tires that we will probably race at Silverstone.
"I think this is an advantage over all the other teams," added the triple world champion.
Monaco winner Rosberg, however – who actually drove at the Barcelona test with his teammate Lewis Hamilton – disagrees, insisting Pirelli had full control of the running.
"We have no say whatsoever — they (Pirelli) say 'you are doing that, that, that and that' and the engineers that they have run our program," he told Sky Sports.
"So it is not for us to learn anything or to decide on anything that we do."
Vettel also scoffed at Pirelli's decision to merely test proposed changes to the tire design this weekend in Canada, because of the lack of unanimity up and down pitlane.
"The tread completely falls off," said the 25-year-old. "This is a safety risk for all of us.
"That we won't have these (revised) tires for the race on a fast track like Canada, for me is inexplicable," added Vettel.