Smith, a left-hander acquired from the Royals last winter, was charged with his first run of the season on Tuesday in his 15th Brewers appearance. Allen Craig's RBI triple off Smith tied the Brewers-Cardinals game in the seventh inning, but the Brewers went on to win in the 11th.
It left Francisco Rodriguez, who has a 0.00 ERA through his first 16 appearances, as the only Brewers reliever yet to surrender a run.
"I never thought I would get through the season without giving up a run," Smith said with a shrug. "My job when that happens is to get people out and try not to give up [more] runs."
Entering Wednesday, Brewers relievers had a 2.16 ERA, trailing only the Padres (1.81) and Giants (2.06) in the Major Leagues. Opponents entered the day hitting .194 against Milwaukee's relievers.
"I don't think it's surprised us; we believe in ourselves and we believe in each other so much," Smith said. "We feel like we can shut down anything, any time we go out there. It's a lot of fun."
Smith has mostly been a starting pitcher in his career, and he said the heavy workload so far has not presented any problems.
"This is kind of a break for my arm," Smith said. "I don't mind it. Hopefully, it's only 10-15 pitches every outing. I still feel fine every day."