Simon Yates lost more than a minute to his rivals, including fellow Briton Geraint Thomas, after suffering from cramp on stage two of Tirreno-Adriatico.
Last year's winner Yates (Team Bike Exchange) was part of a breakaway but fell back late on as Ineos Grenadiers' Thomas surged up the final climb.
The Welshman was then overhauled by faster finishers, as world road champion Julian Alaphilippe beat Mathieu van der Poel and Wout van Aert to the line.
"[Yates] just had some cramps," said Team Bike Exchange head sporting director Matt White. "He had a big off last weekend at Strade Bianche.
"He's gone deep today, and he couldn't hold the group because of the cramp. But the bigger picture is the Giro [d'Italia], where we're going [there] to win."
Following the departure of twin brother Adam Yates to Ineos, Simon has announced a busy schedule for 2021, which includes the Giro, aiming for stage victories at the Tour de France and selection for the Olympics.
He now has a one minute 34 second deficit to leader Van Aert overall.
"We're certainly out of the game to win [overall] here," added White. "But I think his form is good and we know he has the talent."
At the end of the hilly 202km stage from Camaiore to Chiusdino, Alaphilippe (Deceuninck-Quick Step) stayed ahead of two of the most in-form riders in cycling in Van der Poel and Van Aert, who won Wednesday's opening stage.
Last year's Tour de France winner Tadej Pogacar of UAE-Team Emirates came across the line in fourth.
Thomas finished the stage in 13th but stays in contention for the general classification just 14 seconds behind Jumbo-Visma's Van Aert, who keeps the leader's blue jersey for Friday's hilly 219km stage from Monticiano to Gualdo Tadino.
The highest placed Ineos rider is Pavel Sivakov, 11 seconds down on the overall leader, but both Thomas and 2019 Tour-winning team-mate Egan Bernal are expected to be protected for the overall win.
Elsewhere, Ireland's Sam Bennett won the sprint on stage five of Paris-Nice.
Green jersey wearer Bennett took his 53rd career victory in style, powering to the front of the peloton inside the final 200m.
Jumbo-Visma's Primoz Roglic remains in the yellow jersey, 31 seconds ahead of Bora-Hansgrohe's Max Schachmann. Tao Geoghegan Hart abandoned the race on Wednesday following a crash.