Street is competing with Manuel Corpas for the closer role, a job he held in Oakland last season, but is not worried how the outing is going to affect his chances.
"You can't worry too much about results this early, but I will never get comfortable giving up runs," Street said. "We are just trying to build, to get a little bit better. I was really happy with the outing, except the run. I hate giving up runs. It doesn't matter if it is February 26 or October 26th."
Street came to Colorado in the trade in November that sent outfielder Matt Holliday to the A's, and has 94 career saves, the fifth most in major league history by the age of 25. He was 7-5 with 18 saves for the Athletics last season.
His three hits Thursday in one inning were all singles.
"I was locating my fastball good. I was only unhappy with one pitch, and it was a changeup that gave up a hit," Street said. "I will take the swings they gave me. Right now you are just trying to establish your fastball location, going in and out. You will start putting guys away at the end."
Corpas pitched a scoreless inning in the spring training opener for the Rockies on Wednesday.
"I embrace it," Street said of the competition for the closing role. "I think it is going to be healthy for both of us. It is going to push us both to be better baseball players, which at the end will help the team."
Colorado starter Jason Hirsh, competing for the No. 5 starting spot, allowed six hits and three runs to the White Sox in two innings.
Chicago starter Gavin Floyd, the White Sox No. 2 starter, pitched two innings, allowing a run and three hits.
"Floyd threw the ball really well," Chicago manager Ozzie Guillen said. "It was awesome. He did an awesome job. There was one (fielding) mental mistake at short or he should have thrown a two-inning shutout."
Floyd, who was 17-8 with a 3.84 ERA last year, gave up a double to Jeff Baker in the second inning. Baker later scored on a groundout.
The White Sox have emphasized to Floyd he doesn't have to throw early in spring training but coached were impressed.
"He is going to be better," Guillen said. "I really like what I saw."
Colorado's Omar Quintanilla had two of the Rockies' seven hits.
Colorado first baseman Todd Helton was held out of the second straight game. The Rockies are being careful after he had offseason back surgery. The club has not announced when he will see his first action. ... Rockies utility player Ian Stewart did not play because of a strained left biceps. Stewart, competing for playing time in left field and third base, went 0-for-3 in the spring opener.