Niersbach praised the team's stability after reaching their fourth consecutive semi-final in a major tournament and said anything beyond this stage would be a bonus.
Germany have never beaten Italy in a major tournament in seven attempts.
"Reaching the last four for the fourth tournament in a row is a sign of continuity and stability," Niersbach told reporters at the closing news conference at their base in Gdansk.
"It is the federation's wish - it is not a demand but specifically a wish - that we finally reach the very top once."
"Whatever comes after this stage is a bonus and it will not be the end of the world if we do not win because the overall picture is already positive for us."
The three-time European champions have again fielded the youngest team in the tournament, just like at the 2010 World Cup, but have not won a major trophy since Euro 96.
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