After the game, Pagan said the tightness prevented him from swinging "100 percent" in batting practice.
"I have no idea," Pagan said when asked how far away his return is. "I'm just going out there, being positive and hopefully soon I'll be ready.
"I'm all right. I wouldn't say great, but I'm OK."
Pagan has the highest batting average among Giant regulars at .307, to go along with three home runs, 19 RBIs and 11 stolen bases.
"They're the guys who make you go," Bochy said of the top of the order, "and he [Pagan] is our catalyst. He's the guy that really keeps us on track offensively."
The Giants are 2-5 in the games Pagan has missed.
The Giants have been reluctant to place Pagan on the 15-day disabled list. If they do, and he doesn't enter another game in the meantime, they could still backdate him on the list a week with a possible return as early as July 1.
Chris Haft is a reporter for MLB.com. Read his blog, Haft-Baked Ideas, and follow him on Twitter at @sfgiantsbeat. Ryan Hood is an associate reporter for MLB.com. Follow him on Twitter @ryanhood19. This story was not subject to the approval of Major League Baseball or its clubs.