The experienced attacker has to settle for a spot on the bench for now, but is hopeful that he will get the chance to shine later in the tournament.
The prolific striker admitted that he did not feel 100 percent fit ahead of Saturday's game with Portugal and took the decision alongside coach Joachim Low that he would not start the match.
"I had a long dialogue with the coach and we both decided this," Klose was quoted as saying by Kicker.
The Lazio front man made a late cameo, replacing match winner Mario Gomez with 10 minutes to play, but had little chance to impress as Germany closed out a 1-0 victory.
Nevertheless, he remains optimistic about his chance to shine, and fully supports his rival Gomez as Low's side aims for European glory.
"All I can do at this point is be patient and wait for my chance," he said. "And that chance will definitely come at some point.
"I don't feel any jealousy toward Gomez. That would be unacceptable. He is in superb form, and once again showed that."
Meanwhile, Arsenal defender Per Mertesacker, who was on the bench for the entirety of the win over Paulo Bento's side, admitted that his substitute role would take some getting used to.
"This is a new situation for me," he told reporters.
Die Mannschaft take on Netherlands in their second Group B game on Wednesday.
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