"The X-rays were negative, so that's good," Teixeira said. "There was only a little bit of plate available. I thought we had rules about that, but that's a different story. I slid and just got my hand in there, and his foot was right on top of the plate."
Yankees manager Joe Girardi said that he does not expect Teixeira to play in Thursday's series finale against the Tigers.
"It's unfortunate. It's a great hustle play on his part," Girardi said. "My real concern was that he dislocated it when I first saw it, because of the way they were holding his hand."
Teixeira said that he thinks the cut would affect him more from the right side of the plate, and is hopeful that the injury will not force him to miss much time.
"You play hard, that's what happens," Teixeira said. "I'm just happy about the win. That was a great team win. Hopefully, I won't be out long and I'll see how it feels tomorrow."
The play started as Brian McCann hit a ground ball that was smothered by first baseman Miguel Cabrera, throwing to shortstop Andrew Romine and forcing Carlos Beltran out at second base as Jacoby Ellsbury scored.
Romine threw wildly to first base, where the ball was tracked down by pitcher Blaine Hardy and fed to home plate. Teixeira got his left hand in under Holaday's tag and immediately protested home-plate umpire Tom Woodring's out call.
Teixeira also said that he thought Holaday was illegally blocking home plate.
"Oh yeah, but you're supposed to as a catcher," Teixeira said. "But you just don't know the rules now. Could I have run him over? I don't know. I was safe, that's all that matters."
The Yankees have challenged 22 calls this year; 17 have been overturned, three have been confirmed and two have been ruled to stand.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.