"Everybody is going to have to do a little something extra, play the game the way we know how," Torre said. "We're not going to be sitting around saying 'What if,' because that's not what we do. We're going to rely on finding other ways to win games."
"It's a tough loss for us, no doubt about it," said general manager Brian Cashman. "He's a special one, but you move forward, because the schedule won't stop for you. We have a lot of talent here, so everybody will have to step up as we move forward."
Melky Cabrera, who was called up earlier this week to replace Gary Sheffield -- who is on the 15-day disabled list with a left wrist injury of his own -- will likely man one of the corner spots, at least until Sheffield returns.
Bernie Williams and Bubba Crosby will also see significant playing time, though it is unclear how Torre plans to use the three players in a rotation.
"We have to take it day by day," Torre said. "Cabrera will play most of the time; Bernie will DH a lot of the time and play some outfield, also. Bubba has certainly given us a reason to play him; he does a lot of good things out there."
Crosby started in right field on Thursday, moving to left when Matsui was injured. Williams came off the bench to play right field.
"To have a guy like Hideki out, it's tough," Crosby said. "You have to stop, say, 'These are the guys we have,' and deal with it. Hopefully we'll get Sheff back soon, but until then, we'll do what we have to do."
"Some role players will have to step up a little bit," Torre said. "We're going to have to dig in and go get 'em."
The Yankees plan to recall outfielder Kevin Reese from Triple-A Columbus on Friday to take Matsui's roster spot, but Cashman said that Reese would be a bench player for New York.
For now, Cashman said he has no plans to pursue a player via trade to replace Matsui, choosing instead to see what the organization's system can provide.
"We want to assess what we have first," Cashman said. "If you go to the trade market, you'll have to spend from your system. Let's see what we have first.
"We feel we have a lot of guys down there that can offer us something from the Minor Leagues," the GM added. "We tell guys in Spring Training, 'The Derek Jeters and A-Rods of the world are going to be looking for you to help when help is needed. Be ready when your name is called.' Some people are going to get their names called here."
Should the Yankees look to acquire a player from another team, names such as Alfonso Soriano, Torii Hunter, Bobby Abreu and Shannon Stewart are sure to pop up.
"We want to make sure we don't have the answer here," Cashman said. "We had a number of young players step up for us last year, so let's find out first and foremost in-house if we don't have people capable of helping us fill holes."
Sheffield is eligible to return from the DL on May 21, though it is unclear whether he will be ready by that date.
"Thankfully, Sheff's return is expected a lot sooner than Hideki's. They're two pretty special players," Cashman said. "His is a short-term issue. How soon after the 15 days, I don't know. Is it 15, 20 or 25? I know one thing: it's not two months."
For now, with Matsui and Sheffield out of the lineup, the onus to score runs will fall to the other stars in the lineup. Jason Giambi believes that he and his teammates must stick to their regular games, because trying to do too much will only bring bad results.
"You can only do what you can do," Giambi said. "This is a game where, if you try harder, you play worse. Guys have to try not to press, do the little things and make those games count.
"If guys start to get out of their game, that's going to be bad for us," he added. "We have a lot of great players on this team. He's a huge part, and hopefully Sheff won't spend an extended time on the DL, but we can't press."