Hannahan does, however, believe umpires should be punished for blatant mistakes.
"I'm just not a big fan of more instant replay," Hannahan said on Wednesday morning. "There's always been that aspect of the human element in there. Umpires are humans. They're going to make mistakes. The game is really fast. It's a job where you're going to make mistakes.
"But I feel like umpires should be held accountable. Players are. If I consistently don't do my job, I won't be here."
In the seventh inning of Tuesday's 6-4 loss to the Yankees, Hannahan sliced a pitch from New York right-hander Phil Hughes down the left-field line. Left fielder Dewayne Wise tracked down the ball and tumbled over the side wall into the stands during a catch attempt. The ball skipped off his glove and rolled away.
Third-base umpire Mike DiMuro jogged by a fan in a red shirt who was holding the ball in the air, and ruled that Wise made the catch. At no point did DiMuro ask to see if Wise had the ball in his glove, and that was the part of the play that irked Hannahan. To the third baseman, instant replay was not the issue.
"A player goes over the stands or a player goes over the wall," Hannahan said, "the first question is always, 'Let's see the ball.' I feel like umpires would go about their job differently if they knew there were repercussions and that they're held accountable."
Indians manager Manny Acta said that more replay could be beneficial.
"I think it's in the works," Acta said. "It's probably going to be expanded. I think it's going to be helpful for just about everybody, because of cases like [Tuesday] night. ... For me, you've got to have a fine line that you don't want to cross. You don't want to take the human element out of the game completely.
"But I'd probably go like everybody else for the catch, no-catch plays in the outfield, or foul or fair down the lines. Stuff like that. You can't just replay everything."