Cliff Floyd led off the fourth inning with a hard grounder between first baseman Jason Giambi and Cano. Giambi dived and the ball went off his glove and into right-center field. Cano didn't immediately go after it and Floyd beat right fielder Xavier Nady's throw to second for the unusual double.
"That's a ball that we have to hustle after and get and keep Cliff Floyd from getting to second," Girardi said after New York's 8-4 victory.
The Yankees open a four-game series against the Chicago White Sox on Monday night, and Girardi said he hadn't decided whether Cano will be in the lineup.
"Sometimes I let the team down," Cano said. "Ninety-nine percent of the time I play hard. It's kind of frustrating not helping the team, and he's right."
Cano is nearing the end of a disappointing season, batting .260 after hitting over .300 in each of the previous two years. He admitted that he sometimes carries his frustration at the plate over to the field.
This gaffe was particularly rough on the 25-year-old Cano.
"That's embarrassing," he said. "You're playing and you're taken out of the game. ... It's a situation that no player would like to be in."
Cano also was elbowed in the head by Floyd in the second but was OK.
Oft-injured Yankees pitcher Carl Pavano (3-1) also was fine after leaving with a stiff left hip. He allowed three earned runs and five hits before he was booed off the mound in the sixth inning following a visit by a trainer and Girardi.
Pavano was pitching to Eric Hinske with one out and a runner on first when he got the mound visit. After a short discussion, the right-hander walked off as the sellout crowd, familiar with his injury history, showered him with boos.
"I'm at a spot right now where I'm starting to wake up muscles I haven't used in a while," said Pavano, who expected to be OK for his next start. "Every time I go out there, there's more innings than the last time and more pitches than the last time so I mean these are things I'm going to have to work through."
Pavano has started only 24 games for the Yankees since signing a four-year, $39.95 million contract before the 2005 season.
"He did not want to come out," said Girardi, who opted for the safe route on a muggy day in the Bronx. "He told me he was fine."