Defender Heiko Westermann became the latest victim for the three-times World Cup winners when he was injured in stoppage time during their 3-0 win over Hungary on Saturday.
Christian Traesch also dropped out of the 27-man squad after starting keeper Rene Adler and midfielder Simon Rolfes were ruled out.
"The team cannot be allowed to be influenced by these injuries," Lahm, named as captain only last week, told reporters at their training base in northern Italy.
"The big aim is the semi-finals but you first have to deal with the group stage. We want to get into the semis and the team does indeed dream of more than that," he said.
"We have a big tournament ahead of us and we know we have a good team. Those leading players in the squad must make sure no doubts surface," Lahm said.
"The atmosphere here is extremely good. With so many younger players in the team, they seem to bring in some fresh air. The mood is very good," the 26-year-old said.
"For a player it is easier if he always plays in the same position and I would prefer to play right. Don't even think I would play as a defensive midfielder. I have played that position only once in six years," he said.
