Trentin took gold in a four-man dash for the line, outpacing Dutch rider Mathieu van der Poel, who took silver, and Belgian bronze medal winner Wout van Aert after five hours 50 minutes of slog in the rain over 230.4km in the awkward conditions.
Slovakia's Sagan, who suffered with injury last month en route to winning a sixth points classification title at the Tour de France, was two minutes 45 seconds down on the leaders when he abandoned the race on the 11th of 16 laps of the looped course.
He had also already been forced to chase back earlier after being held up by a lengthy wheel-change.
"I was not in good shape and I still have a lot of pain from my crash at the Tour De France a few weeks ago," he said.
"It was a very technical course and it was really hard. In the end, I still felt a lot of pain in my back and in my hip. I think I really needed more time to recover for this race."
(Reporting by Ian Chadband, editing by Pritha Sarkar)
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