Dempster threw four shaky innings in his final spring start and Chicago lost to a Colorado Rockies split squad 6-4 on Sunday.
Tyler Colvin hit a grand slam in the eighth for the Cubs to make it close. It was Colvin's third homer of the spring.
Clay Mortensen, expected to open the season in the minors for the Rockies, worked five shutout innings and gave up three hits.
Jose Morales, trying to win the backup catcher job in Colorado, had a two-run double off Dempster in the second and an RBI double in the fourth.
Dempster, set to pitch Friday against Pittsburgh at Wrigley Field, allowed three runs and five hits. He walked two and struck out two, throwing 73 pitches.
"They had a lot of lefties, and I got to throw some good splits. I was able to go about my business and get ready for Friday," the right-hander said.
Dempster finished the spring 1-1 with a 2.57 ERA. He said he's looking forward to facing the Pirates at home.
"It's a tremendous honor," he said. "There's probably more leading up to it, but once that first pitch is thrown, it's just like any other game. I'm going to treat it like any other start and just be prepared. It's an honor to go out there and do it and hopefully get us a 'W.'"
NOTES: Chicago catcher Geovany Soto had two hits. ... The Cubs released veteran right-hander Carlos Silva, bringing their spring training roster to 27. Silva was let go after making critical comments Saturday about first-year pitching coach Mark Riggins. "Basically, he wasn't good enough to make the team," general manager Jim Hendry said. "Besides that, his comments about Mark Riggins were totally inappropriate and unacceptable. Once again, it's a weakness for somebody that doesn't perform well and chooses to blame somebody else on the way out." ... The Rockies reassigned seven players to minor league camp: second baseman Eric Young Jr., catcher Jordan Pacheco and pitchers Matt Daley, Greg Reynolds, John Maine, Rex Brothers and Eric Stults.