But they also recognized that the difference between winning and losing had only a small amount to do with the pitch that sailed from Chad Gaudin's right hand; it was just the final mark on a laundry list of reasons the Yankees suffered a 6-5 loss to the Rangers in 13 innings on Friday.
"It's a long game -- we had opportunities to win," Yankees manager Joe Girardi said. "No losses are fun. We're going to lose some tough games, and this was a tough one."
Opening a series that could serve as a preview of things to come in October, Cruz commanded a starring role, slugging a game-tying home run in the eighth inning off Joba Chamberlain before coming back five innings later to deliver the game-winning shot.
"It was a slider and not a very good one, obviously," Chamberlain said. "He took a good swing. We're not in that position if I can make my pitch."
The second homer came off Gaudin, who had entered as New York's eighth pitcher during a contest in which the clubs tied an American League record by using 19 hurlers, with Cruz's 19th homer fueling Texas' ninth walk-off victory of the season.
An elated crowd of 46,179 -- many of whom hung around for the postgame fireworks -- enjoyed the course of the five-hour, 12-minute affair, which featured the Rangers' never-ending supply of hurlers who seemed able to evade damage, time and time again.
"Exhausting," Texas third baseman Michael Young said. "We were all pretty much gassed. This one was a big one to win. Our bullpen did an incredible job, and then Nellie picked us up."
The Yankees enjoyed a four-run third inning that seemed to have their efforts pointed in the right direction, but they would head for the showers having seen their lineup go 3-for-17 with runners in scoring position.
"We left a lot of guys on base," said Yankees shortstop Derek Jeter, who went 1-for-7 and grounded out with the go-ahead run at third base in the 12th inning. "When you're playing good teams and you get those opportunities, you've got to get them in, and we weren't able to do that."
The Yankees chased left-hander C.J. Wilson after just three innings, working deep counts and notching timely hits in a four-run third, even as Texas' No. 9 hitter, Julio Borbon, rolled to set a new career high with four RBIs.
In the productive third inning, Alex Rodriguez started the damage with a two-run double up the gap in right-center field, scoring Nick Swisher and Mark Teixeira, and Marcus Thames and Francisco Cervelli added RBI singles in that frame.
It spelled the end for Wilson, who yielded to the bullpen, beginning a parade of 10 Rangers relievers. But the Yankees felt comparatively comfortable in the pitching department, as Javier Vazquez offered a decent start.
Vazquez later displayed terrible body language as he discussed the start, slumping in his locker and talking about how he was not only disappointed with the four runs on six relatively soft hits, but also that the Yankees had cut short his outing after 88 pitches and five-plus innings.
"I don't have to prove myself," Vazquez said. "Whatever they want to do, they do. It's disappointing, but I can't do anything about it."
At least one person in the Yankees clubhouse believed a turning point in the game had arrived early.
The Rangers scored their first run in the second inning following what they saw to be a blown call at second base, as umpire Alfonso Marquez ruled that Jeter missed the tag on an Ian Kinsler stolen-base attempt.
Jeter flipped the ball to second baseman Robinson Cano, only to hear the crowd roar as a surprised Kinsler was ruled safe. Jeter asked Marquez how he could have called him safe, Marquez replied that he'd missed the tag, and Girardi soon followed with his own line of questioning.
"He said he didn't tag him," Girardi said. "It's the difference in the game."
Kinsler came home to score on a Borbon groundout, but Jeter wasn't exactly signing up with his manager's assessment.
"That was so long ago -- that was five hours ago," Jeter said. "It happens. People make mistakes. We had a lot of opportunities, and we missed a lot."
Texas added two more in the fourth inning when Borbon came through again, this time lining a double down the right-field line that scored Kinsler and Mitch Moreland. Borbon added a sixth-inning RBI grounder facing Dave Robertson.
Teixeira worked a bases-loaded walk facing Pedro Strop in the sixth inning to force home New York's fifth run. Teixeira was credited with his 100th RBI of the season, marking the seventh straight year the first baseman has reached the century mark in that category.
Phil Hughes made his first relief appearance of the year for New York, hurling a scoreless ninth after seeing his start skipped this series with an eye toward his looming innings limitations.
Mariano Rivera also hurled two scoreless innings out of the bullpen, small positives to take home on a night when the Yankees knew they should have fared better.
"They've got a great lineup from top to bottom, and they can beat you in a lot of ways," Chamberlain said. "They did it with the long ball today."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.