PITTSBURGH -- First annoyed by the Pittsburgh Pirates' mascot, Los Angeles Dodgers ace Clayton Kershaw was further perturbed by the Pirates themselves in his second-worst outing of the season.

The National League Cy Young Award favorite at nearly the season's halfway point, Kershaw was felled by one bad inning Sunday, just as he was in a start April 26 against the Miami Marlins.

Kershaw gave up all four of his runs Sunday in the second inning of a 4-3 Dodgers defeat. On April 26, it was a five-run sixth inning that did him in. For the record, that means nine of the 24 earned runs Kershaw has allowed this season have come in two of his 121 innings.

It was an all-around flies-at-the-barbecue kind of day for Kershaw. He was first seen stretching in the PNC Park outfield while shooing away the Pirates' mascot, who buzzed the Dodgers' ace pitcher with a remote control car as he stretched on the turf.

The real nuisance, though, came from an unexpected source in the second inning. Pirates pitcher Chad Kuhl worked an eight-pitch at-bat before striking out in his first career trip to the plate. Fellow rookie Adam Frazier singled in a run, and veteran David Freese crushed a three-run double to right-center.

Kershaw has set the bar so high for himself that anything less than total dominance looks troubling. The silly reasons include the heat, the humidity, an inability to get comfortable, the night game on a Sunday and whatever else could be used to explain what was akin to a UFO sighting.

"I don't know, you really don't think of being comfortable out there," Kershaw said. "Really, what it comes down to is limited damage. Some of those hits in that inning, you miss some spots, and they really don't hit it that hard. But the Freese hit is what killed you tonight, killed me tonight.

"I missed my spot bad, and he made me pay. He's a good hitter, and he's had some success against me. He's always been a tough out. You have to get the guy ahead of him out, obviously. But yeah, that's pretty much the name of the game tonight."

It was pretty much game-set-match at that point, with the Dodgers getting RBIs from only one player -- Justin Turner -- all night. The three runs the Dodgers scored off Kuhl in his first career start came on a Turner home run in the third inning and a Turner double in the fifth. The Dodgers had just four hits off the first-timer. Against the Pirates' bullpen, they had none.

Although the story always seems to revolve around Kershaw on the days he pitches, regardless of the result, what the Dodgers are really dealing with is a continued offensive problem. Kershaw can't deliver a three-hit shutout every night.

"I don't know how many hits we had -- maybe four hits tonight," Dodgers manager Dave Roberts said when the subject of the elephant in the room was broached. "We hit some balls hard. ... I think, yeah, throughout the lineup we've got to have some more production."

Indeed, the Dodgers hit more balls hard than the Pirates -- if only that were the name of the game.

"We feel like it doesn't matter who's out there, we owe every guy our best effort every night," Turner said when asked if there is a sense that the offense owes Kershaw a night to be a little off. "We just fell a little short tonight."

Kershaw is used to the sky-is-falling routine when he doesn't win a game, even if it was just the Dodgers' second defeat in the 16 times he has been on the mound this season.

"I wish I had an excuse for you," he said. "I just didn't pitch well enough to win tonight."

He was even asked about his struggles with a journeyman catcher in Chris Stewart, who collected two more hits off him. Stewart, a career .235 hitter who entered the game batting .195, is now 9-for-17 against one of the best pitchers the game has ever seen.

"Yeah, he's had some hits," Kershaw said. "You go back and look at some of them. He has hit a few hard. I'm just behind in a lot of counts to him. He does a good job when he's ahead of the count, for sure."

When you're the best, the dissection gets a little closer to the bone. It might not have if the offense delivered just a bit more. The Dodgers have won a few games in which the opponent scored four times. Sunday was not one. Kershaw was stand-up enough, though, to put it all on his shoulders.

Even though Yasmani Grandal was the catcher behind the plate for both Kershaw's bad innings and both of his defeats, he wasn't going to let either of his backstops take the fall.

"Yeah, Yas and I are getting on the same page and doing a good job," Kershaw said. "They don't get the credit when we pitch well, and so they don't deserve the blame when we pitch bad. And that's the way it works."