The reigning National League Cy Young winner left the game with the Dodgers leading, but a combination of four relievers couldn't get the job done.
With Jamey Wright and Brandon League unable to go after throwing two innings each Monday, Mattingly called upon Matt Guerrier, who gave up a game-tying homer in the eighth, and John Ely, who surrendered three runs in the 11th while making his 2012 debut.
"We're at the end of our rope after the last few days of guys that are available," Mattingly said.
The loss drops the Dodgers to 3-1 in September and 1 1/2 back for the second NL Wild Card spot, currently held by St. Louis.
The Giants' own extra-inning loss kept the Dodgers 4 1/2 games back in the National League West.
"It's September," Kershaw said. "It's put up or shut up. We've got to win games, whether it's 4-3 or 14-3."
With all the firepower and big names added to the team, the offense hasn't been able to pound opposing pitching like it was expected to.
The Dodgers are scoring only 3.3 runs per game in their last 10 and slugger Matt Kemp, who Mattingly said isn't playing at 100 percent since his collision with the wall in Colorado last week, is in a 3-for-21 slump since coming back.
"We'd definitely like to win a game 10-0 one time," Kershaw said. "That's everybody's goal right now, but that's the way they've been going."
It looked like the Dodgers were destined for their third straight walk-off win after Adrian Gonzalez and A.J. Ellis delivered heroics Sunday and Monday, but it wasn't in the cards Tuesday night.
After a shutdown 10th inning, Ely gave up a leadoff single to Cameron Maybin, and a bunt by Everth Cabrera set the Padres up for the win. Fielding the well-placed sacrifice, third baseman Luis Cruz's throw to Mark Ellis at first to get Cabrera was off the mark and put runners on second and third with no outs.
Will Venable was intentionally walked after Ely got the next batter out to load the bases, and all three baserunners would score on Logan Forsythe and Chase Headley singles that followed.
An RBI single by Shane Victorino and a sacrifice fly by Gonzalez broke a 1-1 deadlock in the seventh to give the Dodgers a two-run lead with the game handed over to the bullpen. Kershaw had just come out of the game with 116 pitches thrown and the Dodgers in need of a pinch-hitter.
Into replace the lefty for the eighth, Guerrier served up a tying, two-run homer to Yasmani Grandal and any hopes of Mattingly to give his relievers a rest went out the window with the game headed to extra innings. Randy Choate and Ronald Belisario were also called upon to pitch after the Grandal homer.
Things started rocky for Kershaw when he gave up a first-pitch homer to Chris Denorfia, and he allowed a baserunner in each inning, but he worked his way out of a number of jams. However, he buckled down and threw seven innings of one-run ball before falling victim of yet another no-decision.
"It's always nice to get those wins and have something to show for it," Kershaw said. "All you can do is pitch well.
The lefty struck out nine Padres and became the fifth Dodgers pitcher with three straight 200-strikeout seasons, joining Sandy Koufax, Don Drysdale, Fernando Valenzuela and Hideo Nomo.
"We've seen a lot of him over the years, we've watched him grow up before our eyes," Padres manager Bud Black said. "He ramped it up when he needed to tonight."
Andre Ethier hit a solo homer in the second -- his 1,000th career hit -- to tie the game early. Ethier, who hit the game-tying homer Monday night in the ninth, has five in his last 13 games. He had only three homers in his previous 70 games.