"Missing a day here is better than missing two months," Perez said after the game. "I might've pitched in the past. ... I always want to pitch. I always want to be up. But I felt a little better today knowing we have good arms down there."
Perez said he expected to be available for Monday's doubleheader with the Yankees.
Perez logged 22 pitches in a dramatic ninth-inning save in Saturday's 7-6 win over Detroit, giving the two-time All-Star six saves on the season. Through 13 appearances, the right-hander has gone 1-0 with a 0.69 ERA and 14 strikeouts in 13 innings.
During Spring Training, Perez missed a significant amount of time due a right shoulder injury, but he said this latest incident is unrelated to that.
"It's definitely different," Perez said. "It's a different part of the shoulder."
Prior to Sunday's game, Francona met with Perez and asked the closer to be honest with how he felt during the game, given that the closer worked an intense save the previous night. The manager said he appreciated that Perez was honest with him.
"He was really good about it," Francona said. "After he got up and threw, he said, 'You know what? [the shoulder is stiff].' I thought he used very good judgment. He was feeling it. I just don't want it to lead to an injury."
Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. This story was not subject to the approval of Major League Baseball or its clubs.