"I hurt it the second at-bat," Mesoraco said, referring to a groundout in the fourth inning. "I felt it about three-quarters the way down the line. I had a hard time running from there on out. I was able to catch, it didn't bother me back there a ton. I stayed in there. Definitely running wasn't too great."
Mesoraco, who was replaced on Wednesday by backup Tucker Barnhart, is viewed as day to day.
Cozart exited Monday's game before the bottom of the fourth inning with tightness in his lower right quad. He had reconstructive surgery on his right knee in June, and because he is sore in the same leg, did not want to take any chances.
Following treatment during Tuesday's off-day and again on Wednesday afternoon, Cozart was doing well.
"I feel way better," said Cozart, who was replaced in the lineup by Ivan De Jesus Jr. "When I came out of the game, I could barely lift my leg up, to be honest with you. I came into the training room yesterday and today to do some more training room stuff. I loosened everything up in the quad area. It was so tight and locked up that I couldn't do anything. I'm feeling way better today. I already hit, felt fine. Definitely, it's positive."
Both Cozart and Mesoraco got into Spring Training games later than others because they were finishing their rehabilitation, and Mesoraco had a setback with soreness in his left groin.
Manager Bryan Price does not believe that either player's health would give him long-term concerns.
"It's just that point in time of the season where it's cold and the guys have a hard time staying loose. That's the biggest challenge we have right now with the weather," Price said. "It's certainly going to be better in St. Louis [for the next series], it's supposed to be at or near 70 degrees all three days that we're there. Dealing with the cold weather in Cincinnati and Chicago so far has been more challenging for guys coming off these surgeries."
More injury updates:
• Homer Bailey (Tommy John surgery) was hit in the foot by a line drive while pitching in an extended spring game on Monday. It is not known yet when Bailey will resume pitching, but he could work one more simulated game before beginning a rehab assignment.
• Pitcher John Lamb, who is trying to return from December back surgery, could begin a rehab assignment with Triple-A Louisville as soon as this weekend. Lamb pitched three innings at extended spring on Monday.