"It doesn't matter now. I can't really do much about it," Giambi said.
Nor could the Yankees accomplish much against Royals right-hander Kyle Davies, which is where the broader focus of the offensive output should fall. The Yankees twice had runners at third base with less than two outs and were not able to bring them home.
Alex Rodriguez bounced into an inning-ending double play in the first. In the fifth, Robinson Cano led off with a double and moved to third on a sacrifice bunt before being stranded there. The final out of the inning was made by Damon, who'd finish the night 0-for-5, snapping his 14-game hitting streak.
Later, it was those missed opportunities upon which Yankees manager Joe Girardi would wistfully look back.
"Those are the opportunities that hurt," Girardi said. "You have to take advantage of those situations."
Still, the Giambi strike three call endured most prominently. After Montague's call, Girardi could clearly be seen gesturing at Montague from the Yankees dugout, yelling, "Come on, Eddie!" Giambi rarely shows such animation to an umpire, and he would later sidestep questions, saying, "I love and respect Ed Montague."
"From where I'm sitting at, it didn't look like he went," Girardi said. "We lost the game on missed opportunities. It is a big part of the game, but umpires are doing their best effort. Players are doing their best effort.
"You have to take advantage of your opportunities -- you can't take it out of the hands of everybody else. You have to win games yourself."
Rasner lost for the third consecutive start, though he deserved a better fate. The 27-year-old right-hander was hit around early, allowing leadoff doubles in three of his first six innings, but limited the damage to two runs.
Faced with a rising pitch count, Rasner was inspected on the bench and sent out for the eighth inning, logging a career-high 118 pitches -- the most thrown by a Yankees starter this season. He set down the last eight Royals to face him.
"He was great tonight," Girardi said. "Our bullpen was somewhat depleted tonight and we needed eight innings out of him. What can you say about the guy? He's pitched well really almost every game."
Had Giambi walked on the 3-2 pitch from Mahay, perhaps the Yankees would have scored and either taken Rasner off the hook or put him in line for a victory. Instead, the Yankees were again quiet, scoring a combined three runs in his past three starts after putting up 21 in his first three.
"I'm just waiting for these guys to break out," Rasner said. "It's just a matter of time before they put up eight, 10, 12 runs -- who knows? I'm not changing the way I pitch, I'm just going out there and trying to get them back in so they have a chance to score."
After effective use of his changeup helped Davies throw up six blank innings, the Yankees finally broke through in the seventh. Cano drove a one-out double to right-center field and, after a flyout, scored on Melky Cabrera's single to right field, chasing Davies after 104 pitches.
But Mahay quenched the rally with 1 1/3 innings of scoreless relief, setting up the ninth inning for Royals closer Joakim Soria, who got the first two outs before allowing a single to Cabrera, keeping the game alive.
Keeping his saves record perfect at 13-for-13, Soria then got Damon to ground into a fielder's choice to shortstop Tony Pena -- inserted as a defensive replacement an inning earlier -- on a ball that nearly skipped up through the middle of the diamond.
"I thought there was a chance, but Tony Pena taught his son pretty well," Damon said, referring to the Yankees' current first-base coach. "He's got some pretty good range. We keep our grass pretty high here, so things weren't in my favor right there."
The loss dropped the Yankees back one game below .500 at 30-31, and they have now lost six of the past seven games in which they entered the contest at the break-even mark, according to the Elias Sports Bureau.
"We've just never really got on that run," Giambi said. "Hopefully, we will. We've got everybody back in the offense, and hopefully, it's coming. We can do it. We know we can do it; we've got confidence in this room. The biggest thing is just making it happen."