Parra and Lucroy both went 2 for 4 in a 5-0 loss to San Francisco on Wednesday, sending the Brewers to their sixth loss in eight games. The rest of the lineup was 2 for 23.
"We didn't get anything going," Brewers manager Craig Counsell said. "There are going to be stretches during the season when you run into pitchers who throw a good game. (Jake) Peavy did a nice job. He got us to chase in the zone."
The Brewers are averaging 2.1 runs a game over their latest skid and scored half of their 20 runs in two of the games. Milwaukee averages 3.95 runs a game overall. They were shut out for the third time in five games and the 12th overall.
"It's mostly the course of the season," Counsell said. "We'll score runs again."
Mike Fiers (5-9) turned in a quality start, taking a two-hitter into the seventh. He gave up hits to Matt Duffy and Hunter Pence to start the seventh and was then replaced by Will Smith, who gave up hits to three of the four batters he faced.
"It was still a great outing even then," Fiers said. "Six innings, two runs. That puts us in a good spot to win a ballgame. They pitched a little better than we did. The one inning got away from us."
Pence's double against Fiers scored Duffy, breaking a scoreless tie.
"He looked real good until the seventh," Lucroy said of Fiers. "They had seen him a couple of times and they made adjustments. A couple of bad pitches. That was it."
Hunter Strickland (1-1) retired three batters for the win, his first since Sept. 27, 2014.
Parra extended his hitting streak to 13 games, matching his career high as the Brewers went 0 for 8 with runners in scoring position.
San Francisco's defense played a big part in that.
Pence chased down Hernan Perez's deep fly to the gap in right-center for the first out in the third, then doubled up Lucroy trying to tag up from second base on Ryan Braun's fly out in the fourth. Left fielder Nori Aoki followed with a tumbling catch near the foul line to end the inning.
Neither team did much until the Giants sent 10 men to the plate in the fourth.
Fiers struck out five and gave up two runs in six-plus innings.
Peavy gave up four hits and had three strikeouts over six innings but left without a decision. Peavy reached on a single in the third — San Francisco's first hit of the game.
Brewers: Braun returned to the lineup after missing two days with tightness in his lower back. Braun went 0 for 4 while batting third. "He was healthy. I thought he was fine," Counsell said.
Giants: 2B Joe Panik (back stiffness) was rested. ... C Buster Posey was given the day off. "They've been going hard since the All-Star break," manager Bruce Bochy said. "I'm trying to keep these guys as fresh as I can."
Brewers: RHP Jimmy Nelson (8-9) will seek his first career win against the Cubs when he faces them on Thursday night in Milwaukee. Nelson is winless in four previous starts against Chicago.
Giants: LHP Madison Bumgarner (11-5) pitches the series opener in Texas on Friday night. He'll be facing the Rangers for the first time since beating them in Game 4 of the 2010 World Series.