Yates was with the main peloton making his way through the final gravel sector of the day when the puncture occurred. He got a quick wheel change from teammate Damian Howson, but with less than 16km remaining the pace on the front was high, and Yates wasn't able to regain contact with the bunch, coming in 1:12 down on stage winner Julian Alaphilippe on the uphill finish in Gorraiz.
"I couldn’t have punctured at a worse moment," Yates said in a statement published on the team website. "We rode well as a team all day, stayed in good position and out of trouble on the gravel sections, but unfortunately all that can disappear when you have some bad luck."
Yates slipped from fifth overall after his solid result in the opening time trial to 36th overall after crossing the line 51st on Tuesday. He's now 1:31 behind overall leader Max Schachmann (Bora-Hansgrohe), who leads Alaphilippe by five second and Team Sky's Michal Kwiatkowski by 10.
"As of right now it’s a pretty frustrating situation, but as a team we’re in good shape and motivated to do something," Yates said. "We just have to wait for an opportunity to present itself and then we will be going on the offensive."
Yates was the team's go-to leader after finishing second overall at both Volta a Catalunya and Tirreno-Adriatico. The 26-year-old Briton has already collected two wins in Spain this season, with stage victories at Volta a la Valenciana and at Catalunya. Mitchelton-Scott's best-placed rider at Pais Vasco is now Mikel Nielve in 25th place at 1:09 down.
Team director Julian Dean said the puncture came at the worst possible moment of the race, as it was so close to the finish and the last pavè section.
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"So it was hard to get a quick change, and getting back in to the race was always going to be an enormous challenge," he said. “All the right riders stopped; Nieve stayed in the front and they gave it everything, but the race was already going ahead with Astana and Sky riding, so it was just pure bad luck."
Despite the bad luck, Dean said Mithelton-Scott wouldn't lower their goal of reaching the podium.
"There's still hard stages left, so Mikel is probably our option now, but Adam is certainly not out of the race and stage wins are still an objective," Dean said.
"The gravel sections themselves weren't too problematic. They were somewhat uncharacteristic for a race like this to have that, but the final circuit itself was quite technical and complex, so if you add that to the gravel then it was a pretty intense final 55kilometres.
"That's bike racing, the boys did good and there’s nothing more we can ask for."
