Crisp was injured trying to beat out an infield grounder in the 13th inning. Anderson aggravated his ankle in the 18th inning trying to field a ball.
Anderson was scratched from Monday's start but wound up pitching 5 1/3 innings in his first career relief appearance. He's 1-4 with a 6.21 ERA in six games.
"I kind of needed to step up for the bullpen's sake the other day, do a job there," Anderson said. "But now it's time to let this thing heal up once and for all and get ready to make a run where hopefully I can stay healthy and pitch good."
Crisp was hitting .283 with five home runs and 12 RBIs in 24 games.
"In Coco's case, he came in yesterday, there was some discoloration," manager Bob Melvin said. "Certainly wasn't in a mode where he could run. He was having a little trouble walking, and [he is] a guy that uses his legs so much, and hamstrings can be tricky deals."
Catcher Luke Montz and right-hander Dan Straily were called up from Triple-A Sacramento to take their places.
"Our front office felt like this was the guy, and talking to [Sacramento manager] Steve Scarsone and the development staff, a guy that was swinging the bat well against left-handed pitching," Melvin said of Montz. "We do have, I think, five lefties coming up in the next 12 days or something like that. The feeling was to get him here and get him some at-bats against left-handed pitching."
Montz, penciled in as the designated hitter and batting eighth, will make his first Major League appearance since 2008, when he was with the Washington Nationals.
Straily was recalled Monday to make the start in Anderson's place. He was on the A's Opening Day roster and has made two starts for Oakland.
Rick Eymer is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.