Rosberg is 28 points behind double Formula One world champion Hamilton and came to Monza needing to claw back points before the championship heads out of Europe to races that are among his rival's strongest.
Instead, the German will start fourth with the Briton on pole position for the 11th time in 12 races, although with doubts also hanging over Hamilton's engine pending investigations.
The Mercedes mechanics had to work flat out between final practice and qualifying to replace Rosberg's engine with one that had been used in five previous races.
He avoided any penalty, because it remained within his quota for the season, but Mercedes had brought an upgraded engine to Monza for both drivers and the change meant reverting to a less powerful unit.
"We realised directly after P3 (final practice) so the mechanics did an incredible job to change everything in one and a half hours or something," Rosberg told reporters.
"It has a lot of mileage, it's done six races...and engines degrade over time so it definitely has compromised my weekend and will compromise my race as well.
"You can see that I lost a lot of time on the straights," added the German who hoped to be able to race the two Ferraris ahead of him but was less sure about catching Hamilton.
Mercedes motorsport head Toto Wolff said, however, that the team had yet to discover the cause of the problem and Hamilton's engine could not be given a clear bill of health yet.
"It was clear today that even if we would have found out what the problem was, we couldn't change two engines so we did it on Nico's car," he said.
"If we find out that it is a major issue and this is something that would put Lewis's engine or race at risk, this would be certainly something that we would consider," he said of the possibility of Hamilton's engine also being swapped out.
"Our car has great pace and it's better to play it safe."
Wolff said Rosberg had struggled with understeer which could also be linked to the engine change.
"I would say the combination of an old engine and a car that wasn't properly set up to these conditions made him end up in P4."
(Editing by Tony Jimenez)
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