Nibali launched an attack on the Poggio, marking a move by Krists Neilands (Israel Cycling Academy) and then riding free with 6.4km remaining.
"We were in the front on the Cipressa and Poggio, but when Nibali went, we fell asleep a little bit there. Pretty much the whole bunch, just let him go and he gained 15 to 20 seconds," Kwiatkowski told Cycling Weekly.
"I was surprised that none of the other sprinters' teams were going, they just stopped riding. I thought they were going to make a steady tempo without any slowing down or any crazy accelerations."
Kwiatkowski said that he attacked a couple of times on the Poggio climb, where he was marked by Peter Sagan (Bora-Hansgrohe) and once on the descent, but that Nibali was riding clear.
Former winner Alexander Kristoff (UAE Team Emirates) had team-mates and Caleb Ewan (Mitchelton-Scott), who placed second, also had team-mates, while Quick-Step Floors tried to organise for Elia Viviani.
"I thought the sprinters' teams were going to catch him," Kwiatkowski added. "Gianni [Moscon] was there, but after so many kilometres, it's really hard. We could've cooperated more, but it's up to the sprinters' teams at the end of the day to chase Nibali back. We were only two guys, but there were other teams with more than two. What can we do?"
Team Sky lost Lukasz Wisniowski in a crash, but Kwiatkowski relied on his other team-mates, including Luke Rowe battling back from a leg fracture last summer.
"Luke Rowe was impressive, chasing the break all day and then working on the Capo Mele, Capo Cervo and Capo Berta," Kwiatkowski continued.
"I felt great the entire race, it was amazing to take the responsibility, we did well with that, we were at the front at the right moments , but it's tricky to be in the game in San Remo, you need to have some luck and really feel the moves, how the peloton is going to go. Nibali was the best today, but I expected something more from myself. It's a pity."
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