Mets manager Mickey Callaway admits that the error in lineup order "probably cost" the Mets the game. (1:09)

A potential first-inning rally ended prematurely for the New York Mets because they batted out of order Wednesday after a discrepancy in lineup cards. They went on to lose to the Reds 2-1 in 10 innings at Cincinnati.

"It's frustrating," Mets manager Mickey Callaway said. "It probably cost us the game. We had a chance to score in the first, and we didn't."

After Wilmer Flores struck out for the second out of the inning, Asdrubal Cabrera reached on a ground-rule double that bounced into the stands in left field.

Reds interim manager Jim Riggleman immediately approached plate umpire Gabe Morales with his lineup card.

After a brief exchange, Morales ruled Jay Bruce, the next batter in the Mets' lineup, automatically out to end the inning. Bruce officially was ruled out as 2-unassisted, and Cabrera was not credited with a double in the scorebook.

In the lineup posted publicly and on the wall in the Mets' dugout, Flores was batting second, with Cabrera batting third. But in the handwritten lineup card presented to umpires, Cabrera was batting second, followed by Flores.

Callaway said his intended lineup was the one presented to the umpires. The other one, inputted into a computer, was wrong. He did not say how the mistake was made.

play 1:25 Laughing at the Mets' batting order snafu The Dan Le Batard Show finds humor in the Mets batting out of order during Wednesday's game.

"I knew right when they went up there that we were out of order," Callaway said. "It was an administrative thing that I didn't take care of. Once they announce you, you can't do anything."

Riggleman offered his sentiment.

"I felt bad," Riggleman said. "It's so easy to have that happen."

Nearly 10 years ago to the day, it happened to the Reds against the Mets at Shea Stadium. Cincinnati batted out of turn in the ninth inning after a double switch during an 8-3 loss to the Mets on May 11, 2008.

While Riggleman said he felt bad for the Mets, the Reds' Twitter account found humor in the mix-up.

Can someone send this down to the third base dugout? https://t.co/htjvJss5k1 — Cincinnati Reds (@Reds) May 9, 2018

Crew chief Jerry Meals had never been involved in a batting-out-of-turn situation in the majors.

"I've seen it in the minor leagues," Meals said. "It's been a long time, 32 years."

The Milwaukee Brewers were the last team to bat out of order, doing so in the first inning against the Washington Nationals on July 4, 2016.

The Associated Press contributed to this report.