The Bury-born rider went in to the final stage leading by 19 seconds from BMC's Richie Porte after victory on Saturday.
But the Orica-Scott rider could not hold it as Porte took 40 seconds out of him in the 18.3km battle against the clock around Lausanne to clinch the win.
Porte's time of 25:06 was good enough for a second on the stage, with LottoNL-Jumbo's Primo Roglic winning in a time of 24:58.
Yates, 24, readily admits time trialling is a major weakness in his armoury as he aims to mature into a Grand Tour contender, and his time here was only good enough for 12th place.
Team Sky's Chris Froome, who fell out of overall contention on Saturday, finished ninth on the stage with a time of 25:44.
Read the original article on Eurosport: Simon Yates second at the Tour de Romandie