The UAE Team Emirates rider was the first to attack in the race, launching off team-mate Tim Wellens' wheel on the Poggio with 6.6km to go. He was then caught by Filippo Ganna (Ineos Grenadiers), Wout van Aert (Jumbo-Visma) and Mathieu van der Poel (Alpecin-Deceuninck), the Dutchman countering decisively one kilometre later.
Speaking after the race, Pogačar said: "I had one goal today and that was to attack after Tim's pull. Tim did a really perfect job today, I have to thank him a lot for setting up this attack in the end.
"I was not strong enough to go solo with four guys, and then Van der Poel attacked, I couldn't follow. He was too strong. Then I was dead to the finish."
On the serpentine descent of the Poggio, Pogačar chased with Ganna and Van Aert, but the trio couldn't close the gap to Van der Poel. The Alpecin-Deceuninck rider crossed the line on the Via Roma with a 15-second advantage, alone as he celebrated his first victory of the season.
Asked if he rued how the the race unfolded, Pogačar said: "No regrets."
"I knew that it was going to be hard and I have high hopes for the coming years for this race," he added. "Last year I attacked four times, this year, just once and I tried to go to the top.
"Mathieu was sprinting at the top. I was already dead from my turn and he opened the gap really fast. Then, on the downhill, he was so [much] better than us. Out of the corners, you could see that he was really sprinting and the three of us couldn't do the same as him."
Pogačar, who has already won Liège-Bastogne-Liège and Il Lombardia, will next line up at a Monument at the Tour of Flanders in two weeks' time. Last year, the Slovenian broke free on the Flemish cobbles with Van der Poel, but was outfoxed in the finale, eventually crossing the line in fourth.
"The best man won today," he said in San Remo, before adding ominously, "and the best man will win in Flanders."
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