Four of Boston's hits off Garcia went for extra bases, with Adrian Gonzalez and David Ortiz pelting RBI doubles in the first inning.
"He didn't have his velocity today," Yankees manager Joe Girardi said. "I think it caused the other pitches to roll a little bit. He was up in the zone.
"He just didn't have his stuff today when he went out there, for whatever reason. We'll continue to work on it and see what's going on. He didn't have the arm speed that he's had and had all Spring Training."
Mike Aviles, Ryan Sweeney and Dustin Pedroia also knocked in runs off the veteran right-hander, who has permitted 14 runs (13 earned) and 20 hits in 12 innings over his first three starts this season, good for a 9.75 ERA.
"I asked him, 'Are you OK physically?' and he said, 'Yeah,'" Girardi said. "Sometimes, pitchers go through these types of things and you just have to find a way to work through it."
The Yankees endured a setback with right-hander Michael Pineda earlier on Saturday, but lefty Andy Pettitte remains on course to rejoin the rotation in the middle of May.
Garcia and Phil Hughes (6.75 ERA in three starts) seem to be the candidates to be bounced from the rotation to make space for Pettitte, and Saturday's start did not inspire confidence that Garcia should be spared.
"If don't pitch the way I have to pitch, that's my problem," Garcia said. "Whatever moves they have to do, they're doing it, no matter what. It's all about me. If I don't pitch good enough, that's my problem.
"I'm not thinking about who's coming back or they'll bring back. It's not my job to worry about it. My job to worry about is pitch good -- that's all."