Rosberg led the opening stint of the race from pole, but his drop down the order began on lap 12, when Fernando Alonso passed him into Turn 1.
He was further demoted by Sebastian Vettel and Kimi Raikkonen soon after.
The tyre degradation of his Mercedes was such that he dropped to sixth place by the finish, just holding off Paul di Resta's Force India in the closing laps.
"I didn't expect it to be that tough," said Rosberg. "I thought we would be in a better position.
"It was really difficult out there, but why? Why on one lap are we so fast and on a long run so slow? It's strange, and it's not just one axle, it's front and rear. Both are struggling and there's no explanation."
Rosberg admitted he was confident after his opening stint that he could hold on at the front of the field, but was shocked when he could not.
"After the first stint I thought 'who knows, maybe I can keep them behind all day?'" he added. "I knew they were quicker but I was quite comfortable and doing what I wanted to do.
"But then I just went backwards so badly. It was unbelievable.
"It's so strange, so inexplicable. I'm working with my set-up just towards the race, not even for qualifying, and we're so fast on one lap and then in the race so slow."
Lewis Hamilton fared even worse in the second Mercedes, finishing a lapped 12th.
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