"I come to do my job," said Rivera, who picked up the loss in the non-save situation (he's allowed 10 hits and four runs in 14 non-save innings). "When I go there, I bring everything that I have, and it didn't work out. Definitely I'm upset and disappointed with the game, but tomorrow's another day."
Girardi pointed to New York's inability to score runs as a significant cause for the loss, the team's third straight and seventh in its past 11 games. The Yankees (44-40) were 2-for-10 with runners in scoring position against the Rangers (44-41) and are 5-for-32 in their past four games.
"You're looking for consistency," Girardi said. "This is a good lineup, and we're just not getting that consistency right now. ... It's not an offense that should struggle like that, but we are right now."
In the bottom of the ninth with Wilson Betemit on first base and no outs, Girardi let a struggling Melky Cabrera, who was 0-for-18 before the at-bat, try to get a hit off Rangers closer C.J. Wilson instead of bunting. Cabrera grounded into a double play, and Johnny Damon grounded out to end the game.
Girardi said he considered having Cabrera bunt, but Wilson had just walked Betemit on four consecutive balls, so Girardi "didn't think it was the right move."
It was only the second time Rivera had given up three hits (Bradley later singled) in an outing this season. Kinsler led off the inning with the double and took advantage of Rivera's relatively slow delivery to home plate to steal third.
"That's more than enough time for me to steal the base, and I didn't want to lose this game," Kinsler said. "So I was going."
Yankees starter Joba Chamberlain struggled early and lasted just four innings, allowing five hits and four walks while striking out six batters. He threw 73 pitches through three frames and ended with 91, 49 for strikes. Chamberlain, who has started six games this season, went deeper in his second start (4 1/3 innings), one limited by a pitch count.
"I'm not going to be perfect every time," said Chamberlain. "You've got to learn and react from it. It's probably a step forward -- look at it like now I know how I feel when I'm not getting out front, and next time I know how to correct it."
Rangers starter Kevin Millwood was effective, yielding one run on five hits and one walk while striking out six hitters in five innings.
"We got nine hits tonight, but we just weren't able to have a big inning and bunch them together," Girardi said. "You have to be able to bunch them together to score runs."
Three Yankees relievers -- Dan Giese (one inning, one hit), David Robertson (two innings, no hits and two walks) and Jose Veras (one inning, no hits and one walk) -- combined to shut out the Rangers after Chamberlain left and before Rivera took the mound.
Robertson, who was called up Saturday, entered in the sixth inning with the Yankees down, 2-1, and stayed in for the seventh after Betemit cashed in on a two-out rally by smacking a first-pitch fastball to left field to score Jorge Posada in the sixth, tying the game at 2.
Robertson's curveball seemed sharper than during his Major League debut on Sunday against the Mets, and he was glad Girardi trusted him in a tight situation.
"I had a few [curveballs] in there," Robertson said. "The other ones, I was getting out of myself and trying to throw them myself. When I stayed compact and throwing them like I was supposed to, they ended up being good pitches. [Girardi] gave me that opportunity. I'm glad I didn't disappoint him. I didn't let a bunch of runs come in."
But on the flip side, the Yankees didn't push many runs across the board, and players like Damon are sensing that, with the All-Star break near, it needs to happen soon.
"The sense of urgency is now," Damon said. "A lot of teams are starting to figure out whether they have a chance for the postseason or not. We're still there. We need to have a really good July. We've seen a lot of young guys here this year, and we feel like we can win with the young guys and the veterans. We'd much rather become buyers than sellers come July 31."