But unlike Girardi, Matheny was not ready to call for significant changes to the way the game is policed.
"I'm not going to take a hard stance one way or another on the replay," Matheny said. "I know the league is doing what [it] can. I also understand speed of play, but we want the calls made right. I think we have some very good umpires in this league, but they're going to miss [some calls], and part of my job when I see what I see is just to let them know and try to defend my guys."
Matheny was forced to do just that in the eighth inning on Monday, after the Giants' first hitter, Gregor Blanco, worked a nine-pitch walk off reliever Shelby Miller. Brandon Crawford followed with a line drive to right-center, where center fielder Jon Jay made a sensational diving catch. Jay fired the baseball to the infield hoping to double up Blanco, who had broken for second base with the pitch.
First baseman Allen Craig caught the baseball on a hop and made a diving stab at Blanco.
Replays showed that Craig applied a tag to the back of the lunging Blanco.
First-base umpire Bill Miller ruled Craig did not make the tag before Blanco scrambled back to first base safely.
"It was a crazy play," Craig said with a shrug. "A diving play in center, he throws it in and I'm diving after [the runner]. It was a tough call. We just didn't get it."
Craig and second baseman Daniel Descalso argued immediately, and Matheny joined the discussion. The umpires briefly converged on the infield, but the call stood: Blanco was safe.
The Giants turned the call into a two-run rally.
"But that really wasn't the game today," Matheny said. "But every once in a while, there's a big play that does change the course of the game, and I'm not against having something else to help get it right. Our guys work hard to make the right plays and execute, so we want things called fairly."
The inning continued to get away from the Cards after that close call. Two pitches later, Aubrey Huff hit a popup to shallow left field, along the line. Third baseman David Freese chased it, then let it drop a few inches fair for a hit.
"That's just a tough play, to be honest," Freese said. "I'm chasing it down, and you kind of lose track of it. I saw it fall -- and it wasn't foul."
Left fielder Matt Holliday, who seemed to find himself in the middle of everything in Game 2, was too far away to provide Freese help.
"It's just sort of a no man's land," Holliday said. "I'm playing deep in left-center with Huff up, and it's a popup over third. It's just one of those deals where if I was going to make the play, I had to sprint headlong and dive. It's just one of those no-man's-land balls."