Jason Heyward delivered the go-ahead run with a single up the middle that scored Michael Bourn from third base.
Parnell said that he threw a fastball down and away to Heyward, who was able to find a hole in the Mets' defense.
"It's a tough lineup, a tough part of the lineup, too," Parnell said. "It didn't go our way."
Parnell's struggles left the Mets with a crushing loss and undid their earlier comeback after a crucial fifth-inning call went the Braves' way.
The fifth-inning drama began with the score tied at 3, one out and Martin Prado on first. Heyward lofted a short fly ball to left field, and Jordany Valdespin attempted to make a sliding catch. The ball dropped ever so slightly in front of his glove, and Valdespin trapped it. Third-base umpire Dale Scott, however, ruled the play a catch. Valdespin quickly got the ball back to the infield, where it was relayed to first base to double off Prado. The Mets began to jog off the field, believing the inning was over.
But the umpires convened and overruled the initial call, awarding Prado second base and crediting Heyward with a single. Manager Terry Collins argued and was ejected.
Scott said that Valdespin's body blocked his view of the ball.
"I never had any evidence that he didn't catch the ball, but I never had a good look at it," Scott said. "I called it a catch."
Mets starter R.A. Dickey said that it looked like a catch to him but admitted he didn't get a good look at the play.
"They may have gotten it right, and if they did, great," Dickey said. "But in the moment it certainly looked like an out, which is a big play."
The Braves took advantage of the call's reversal, as Freddie Freeman drove a two-run double to give the Braves a two-run lead.
The Mets' offense was unfazed by the sudden turn of events in the bottom of the fifth. After Kirk Nieuwenhuis led off the sixth with a groundout, the Mets strung together five consecutive singles. The first three came off Braves starter Tommy Hanson, who was chased after Justin Turner's pinch-hit RBI single plated the first run of the rally.
Collins was happy to see his team rally.
"They had some very, very good at-bats," Collins said. "We fought back."
Hanson allowed six runs on nine hits in 5 1/3 innings. In the first two games of this three-game series, the Mets faced Hanson and Tim Hudson, the Braves' top two starters. Though neither threw six innings, the Mets have nothing to show for it, partially because neither of their own starters went more than five innings.
Dickey didn't fare much better than Hanson, allowing five runs on eight hits in five innings. It was his shortest outing since April 18, when he went 4 1/3 innings in a loss -- also to the Braves -- and marked the third time in four starts he has given up five runs.
Dickey believes his luck will turn and that this is nothing more than a tough stretch.
"Every season has a storm or two in it," Dickey said. "You just kind of have to stay afloat. It'll turn."
The same could be said for the Mets as the second half begins, as they have lost three games in a row and are 3-6 in July.
"We kind of limped into the [All-Star] break, and we're kind of limping out of it," Dickey said.
Ike Davis, who went 2-for-4 with a home run, said the Mets just need to put together a few wins to be right back on track.
"It comes in waves," Davis said. "Sometimes you get the big hits, and sometimes you don't."