Goals from the Bayern Munich defender, Sami Khedira, Marco Reus and Miroslav Klose secured a 4-2 victory for the 2008 finalists at the expense of the Ethniki, who made the score sheet through Georgios Samaras and Dimitris Salpingidis.
Joachim Low's charges will now prepare for a last-four clash against the winner of England and Italy, which will be played on Sunday.
|Germany 4-2 Greece
The full-back, however, refused to be satisfied with what was ultimately a comfortable win, and urged die Mannschaft to improve in the tournament's decisive stages.
"We made it hard for ourselves unnecessarily. We had a lot of chances against a very defensive playing team already at the beginning. We did not score and that made it difficult," Lahm stated to ZDF.
"Then, when we finally got our goal, we did not pay attention and conceded. We made a lot of mistakes and we have to improve that."
Fellow goalscorer Reus, meanwhile, was content with the victory and progression to the last four.
"It was our big goal to reach the next round and in the end we won deservedly," the Dortmund man stated, also showing his delight at having the opportunity to make an impact.
"We had some talks with the coach in the last days. He told me to keep going and that I would get my chance. I kept working and today I got my chance."
Real Madrid midfielder Khedira was also content with the performance, and singled out the German attack for special praise.
"We are very happy, that is obvious. We made it a little difficult. Then we put more speed into our game. At the end it was deserved. We gave the right answer. We created a lot of chances and I think, it was a very good performance," he stated.
"We will see what comes now. Italy or England, that won't be easy. But if we live up to our potential, it is very hard to beat us."