Garza said that he had grown tired of teams brushing back Longoria, who was also hit on Monday by New York reliever Jonathan Albaladejo.
"I hate to be that guy, but someone had to take a stand and say, 'You know, we're tired of it,'" Garza told reporters. "'You can go after our best guy. We'll make some noise, too.' And that's what happened."
Yankees manager Joe Girardi said he hadn't been sure if Garza's pitch was intentional, given the circumstances. New York led, 2-0, with Johnny Damon at first base and two outs in the inning when Teixeira was hit by a 1-1 fastball.
That moved a runner into scoring position for Alex Rodriguez, who struck out swinging. Girardi said he was surprised Garza admitted his intent, but not that the intentional drilling occurred.
"This stuff has been going on in baseball for a long time," Girardi said. "Sometimes you feel a need to protect your players, whether you feel something is intentional or not. But to come out and say it, that's a little shocking."
Girardi said that only Chamberlain would know if his high pitch to Longoria was intentional, and after Wednesday's game, the right-hander said it wasn't. But Girardi said the Yankees couldn't approve of throwing above the shoulders.
"I don't like to see any pitch [from the] neck up," Girardi said. "It could be a curveball that gets away. If it hits right, it could hurt them. That's something we don't condone at all."
Teixeira has been hit eight times in 97 games this season, after being hit seven times in 157 games last year with the Braves and Angels.
Batting .285 with 26 homers and 74 RBIs entering play Thursday, he said that he did not believe he is being hit significantly more this season and chalked up Wednesday's actions to the so-called unwritten code of baseball.
The most memorable of those hit-by-pitches came June 2, when Teixeira was infuriated by what he believed to be an intentional hit-by-pitch from Rangers hurler and former teammate Vicente Padilla.
"When Padilla hit me, I knew it was on purpose, because there was history there," Teixeira said. "But I know Garza wants to pitch me in. Up and in for most lefties is a spot that guys try to get me out.
"He threw it up and in, and it just grazed my shoulder. I took my stuff off and went to first base. I didn't really think about it during the game."