Had it been successful, R.A. Dickey would have had New York's second no-hitter in franchise history, but the appeal was upheld by Major League Baseball on Friday.
Tampa Bay manager Joe Maddon said he believed the original ruling was the correct one.
"I'm sure if there was another hit in that game, nobody woulda said, 'Let's go back and review that and see if it was a one-hitter,'" Maddon said. "I understand why they would do it. We probably would've done the same thing."
Dickey was dominant from that point on in the first inning, retiring the next 22 hitters before an Elliot Johnson grounder forced David Wright to commit an error in the ninth. Two passed balls and a fielder's choice later, Dickey gave up his first run of the game.
Mets manager Terry Collins said after that game the chances of having the hit later turned into an error were "less than five percent."
"Honestly I thought it was a fair call based on how the ball was hit, how it was rolling, the barehand away from him, the fast runner," Maddon said. "There was a lot of components that indicated it was a hit."