"They came in and whooped our butts for three games," Stanton said.
The Marlins have dealt with adversity before, going 8-14 in April.
Despite being swept, the Marlins remain five games above .500, a half-game in back of the Mets and one game behind the Braves. They trail the first-place Nationals by two games.
"It's not like we're going downhill," Stanton said. "A little slip, ain't no problem."
The Marlins are now 21-10 in games in which they hit at least one home run. They entered the game with the fourth-best winning percentage (.700) in the Majors when they go deep.
Martin Prado had a two-run homer and drove in three runs, and Jason Heyward belted two solo shots to power the Braves past the Marlins and into second place in the National League East.
The finishing blow was Michael Bourn's three-run homer in a four-run ninth inning.
Afterward, Marlins manager Ozzie Guillen was in a meeting with members of the front office, and he wasn't available to the media.
Mark Buehrle, effective in six innings, gave up three hits. But one of them was the two-run drive by Prado in the sixth that put Atlanta in front, 2-1.
"They're a good team," Buehrle said. "The most frustrating thing is I made a good pitch on Prado. It was up and in. You just kind of tip your cap to him. ... We came out and were battling back and forth, 0-0 the whole time and we score a run and then that's the last thing we want to do, go out there and give up a run or two, once it's a close game like that. But I made a good pitch. You just got to tip your cap to those guys."
Atlanta left-hander Mike Minor picked up the win, giving up one run in five innings.
The Marlins were limited to three runs in the three games, and now they look to regroup in Interleague Play against the Rays on Friday.
Atlanta handed the Marlins their first three-game sweep since April 24-26 at the Mets.
The game featured the first replay review at Marlins Park. It came in the eighth inning on Stanton's homer off Eric O'Flaherty.
Stanton showed his immense power to all fields, when he lined his shot to right. The ball barely cleared the wall next to the foul pole. It deflected back and then back toward the field of play.
Initially, it was treated like a double off the wall. But the umpires gathered, and they headed off the field to review.
During the review, Stanton stood on second base talking with Dan Uggla, the Braves second baseman and former Marlin.
"He was bringing me negative energy," Stanton said of the conversation with his former teammate. "Saying, 'Nah, it was off the top.' I was like, 'Come on, man, let's go.'"
It didn't take long for the umpires to declare Stanton had belted his 14th home run of the season.
Through five innings, Buehrle breezed along, limiting the Braves to one hit -- a single by Andrelton Simmons in the third inning. But the left-hander was not given much support, and he and the Marlins trailed after giving up the two-out homer to Prado in the sixth.
Reyes' home run, his first as a Marlin, came on his 222nd at-bat of the season. He last went deep on Sept. 27, 2011, when he homered twice against the Reds while with the Mets.
Dating back to last September, Reyes had gone 225 at-bats without a home run before connecting in the fifth inning on Thursday.
Batting right-handed, Reyes lifted Minor's 2-2 offering over the wall in left field. Not by much. The ball actually bounced off the top of the wall and landed in the Marlins' bullpen. The drive was estimated at 355 feet.
The Braves responded in the sixth.
Buehrle recorded two quick outs, but Bourn extended the inning with a single to center. Prado then put Atlanta in front with his two-run homer to left.
"It was a cutter away," Buehrle said of Bourn's key single. "It was one of those ones that was kind of hit back to you and you don't really know, you just see the ball coming at you. It was like a changeup coming back.
"If I had stood up, it probably would have hit me close to the face or I would have caught it. It's one of those ones that's hit back at you and you do what you got to do to get out of the way. I barely missed it, but he put the ball in play and did what he was supposed to do."
The two-out home run again was a weapon for the Braves in the seventh inning. Heyward connected on a blast to center, beyond the high wall and 418-foot sign, to put the Braves ahead, 3-1. The drive was the first allowed by Steve Cishek this season. The right-hander hadn't given up a homer in 24 1/3 innings.
Prado's RBI single in the eighth gave the Braves a three-run cushion. Heyward's second home run of the night came off Edward Mujica in the ninth. Bourn's blast was off Dan Jennings, also in the ninth.
"We scored in the last four innings, and when they scored, we were able to get a shutdown inning," Braves manager Fredi Gonzalez said. "We were able to add on, and one of the things you want to do defensively is when your team scores, you want to shut that other inning down. They weren't able to do it, and we were able to score some runs and add on."