The Giants didn't get a runner on base until the bottom of the fifth when Brandon Belt reached on Ian Kinsler's error, and San Francisco's first hit came on Aubrey Huff's pinch-hit double to left in the sixth.
"Offensively, we just got shut down," Bochy said. "We were off today."
Rangers starter Alexi Ogando left the game in the fourth with a strained right groin after running out a bunt single. Leaving the game after throwing three perfect innings, Ogando was replaced on the mound by Robbie Ross, who pitched four scoreless innings to earn the win.
"He was sneaky," Angel Pagan said of Ross. "His fastball, sometimes it sunk, sometimes it cut. When a pitcher makes his pitch, you have to tip your hat."
Four Texas pitchers combined to give the Giants their second shutout of the series and season.
Lincecum, on the other hand, was erratic from the start, walking three straight batters with two outs in the first inning before inducing a Mike Napoli grounder to get out of the jam. He tossed 30 pitches in the beginning frame and 104 on the day.
"I was just looking to come in and compete against a good team," Lincecum said. "It's just poor execution on some pitches, leaving the ball up in the zone. Not executing, that's the biggest problem."
Following a season-long trend, Lincecum looked at times like the formidable pitcher who won back-to-back National League Cy Young Awards in 2008-09, striking out the side in the second inning. But he followed that by giving up an RBI double to Adrian Beltre that scored Elvis Andrus, who had tripled to deep right.
"I had a good second inning, and I just wanted to keep that rhythm going on, but I didn't and it didn't transfer," Lincecum said. "I just kept running into bumps here and there and I never had any rhythm."
Lincecum now holds a 6.00 season ERA and has gone eight starts without a victory, the longest winless stretch of his career.
"We keep saying he's close, and I still believe that," Bochy said. "But he was off at times today, no getting around that."
Texas followed with a two-run fourth in which a couple defensive miscues aided the Rangers' rally. First, third baseman Pablo Sandoval misplayed Craig Gentry's infield single to third with one out. Ogando came up next with two runners on, looking to bunt over the runners, but the Giants weren't able to field Ogando's bunt toward the third-base side.
"It wasn't his greatest game there," Bochy said of Sandoval. "These are things we're going to work on. He's going to come in tomorrow and do some stuff. He has missed some time, but it's vital that we do a good job defensively."
After Ogando was pulled for a pinch-runner, Kinsler smacked a two-run double to left to put the Rangers up, 3-0.
"Those things come back to hurt you, and they did," Bochy said.
The Giants threatened to get on the board when Huff doubled with one out in the sixth, but a baserunning gaffe by both Huff and Gregor Blanco on Blanco's grounder to the mound resulted in an inning-ending double play.
The Giants are now 2-11 in games in which Lincecum pitches, and he has only recorded two quality starts in 13 outings this season.
"He's staying pretty upbeat, he's doing everything he can," Bochy said. "And that's all he can do, just go out there and give it his best -- and he's doing that. He's going to figure this out, and he's going to be better because of it."