German driver Rosberg has won seven races in a row, including the first four of 2016, while Briton Hamilton has not triumphed since he won his third world title in Texas last October.
Hamilton has also had two engine failures in four races.
Mercedes motorsport head Toto Wolff spoke out against social media critics and conspiracy theorists at last weekend's Russian Grand Prix.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
The team returned to the theme, addressing "the haters, the naysayers, the conspirators" and pointing out how much hard work was done behind the scenes to give each driver an equal chance.
"We have seen a lot of frustration aired online after the mechanical issues experienced in Sochi. We share those same emotions -- but for us it goes far beyond frustration," the letter said.
"There is no 'A' or 'B' team here," it said after chronicling the amount of work put in by more than 1,000 employees at the factory and racetrack to make the team successful.
Rosberg and Hamilton finished one-two in Russia but Mercedes said that had been little short of miraculous, despite appearances.
Some "alarming behaviour" was detected from Rosberg's energy recovery system after his pitstop and, after consulting with the governing FIA, the team told him to switch to a setting that would control the issue.
The water pressure in Hamilton's car then dropped dramatically, and he was told to take it easy.
Mercedes said the champion lost all pressure for the final 16 laps: "We genuinely aren't sure by what miracle the car limped across the line, but we're certainly not going to complain."
The team recognised they had not met their own expectations on reliability, despite winning the last 10 races and 36 of the last 42, but said failures were inevitable in a mechanical sport.
The next race in the 21-round season is the Spanish Grand Prix in Barcelona on May 15.
(Reporting by Alan Baldwin, editing by Toby Davis)
