After striking out Will Middlebrooks, the Padres sent Melvin Upton Jr. to second to pinch-run for Alonso, and Braves shortstop Andrelton Simmons signaled for a pickoff -- which Grilli threw into center field.
"Simmons doesn't set a pick unless he knows he's got the guy, I just made a bad throw," Grilli said after the game. "If the runner stayed at second base, you tell me what would have happened. I think you can figure it out."
Upton Jr. moved to third on the throwing error and then scored a few pitches later after Cory Spangenberg drove him in on a sacrifice fly to left field.
When asked if he would rather see caution exercised on a pickoff in that situation, Braves manager Fredi Gonzalez stood behind his players.
"I let those guys play, man," he said. "They're out there playing, and I'm just sitting in the dugout, you guys are sitting in the stands, and they're watching and they know what's going on.
"I'm not so sure a good throw might have gotten him really at second base, but you have to let your players play. You can't handcuff them, you can't restrict them, and if they decided to make that play, then I support it."
Nick Masset shut the Padres down in order in the 10th inning before Justin Upton got on base for the first time of the game, drawing a leadoff walk off Cody Martin in the 11th. Upton stole second base and Matt Kemp doubled off the left-field wall to give San Diego a 4-3 lead it would extend to 5-3 when Alexi Amarista doubled off Luis Avilan one batter later.
Monday's blown save was just Grilli's second of the season, but the 11th for the Braves -- second-most in the Majors behind Arizona entering the game. The Braves' bullpen has been charged with 13 losses this season, while Braves relievers last season blew 13 saves in total.
"We're confident," Grilli said. "We're working through some struggles and you know, nobody asks us questions when we're going well … tough game."
Carlos Collazo is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.