"It's a bummer for all of us," Klinsmann told the media on Tuesday. "But we're going to make the best out of it. We're going to get him back for this tournament."
Altidore was forced out of Monday's win over Ghana in the 21st minute with what the team has called a strained hamstring. He was replaced in the lineup by Aron Johannsson.
USA vs. Ghana
USA vs. Ghana
There were initial concerns that the injury may be a full tear, but the worst-case scenario appears to have been avoided.
"We have to see how he reacts the next couple of days with his hamstring," Klinsmann said. "We are full of hope that he comes back in this tournament. That's what we work on every day. The medical staff is doing a tremendous job. We still have the hope Jozy will be back. How quickly? That is down to his healing process.
"All you do as a coach is give him a positive hug and tell him 'You'll be back. Stay positive, you'll be back. Don't count it off now.' We'll keep him positive and we have that big hope he'll be back in this tournament."
Although several players seemed to be nursing muscle injuries during the Ghana match, Klinsmann said none were serious enough to keep them out of subsequent games. Klinsmann even declared Matt Besler, who was pulled at halftime, ready to go.
Klinsmann also rejected the notion that his players may have been over-trained in the buildup to the tournament.
"It was the result of a very physical game, very demanding and demanding conditions," he said. "Our preparation went really well. We were lucky not to have any other injuries. We slowed [training] down before that game. Everybody was fresh, everybody was good. Then you hit some individual cases. We're very unfortunate with Jozy. It's a bummer for all of us. We're going to make the best out of it. We're going to get him back for this tournament."