Most of the Germany team stood in silence as the strains of the anthem wafted through the stadium in Warsaw last Thursday, in contrast to Italy's squad who sang their anthem with gusto.
"It is right and proper that players sing along when the national anthem is performed. They play for the German national team and not for themselves," the state premier of Hesse, Volker Bouffier, told the top-selling daily Bild.
Bavaria's premier Joachim Herrmann said: "The German national anthem belongs to international matches and to the national squad. If somebody cannot be bothered to sing it, he should stay in his local club."
In Germany, the federal states decide whether children learn the national anthem at school. In conservative Bavaria it is compulsory, for example, while in Berlin it depends on the choice of individual teacher.
Patriotism can still be a sensitive issue in Germany because of the Nazi regime, World War Two and the ensuing division into a capitalist western German state and a communist eastern one.
"After two dictatorships that violated German symbols and patriotism, many people have trouble dealing with the national anthem," said historian Paul Nolte.
The music for Germany's national anthem was composed by Joseph Haydn in 1797 and the German poet August Heinrich Hoffmann von Fallersleben wrote the lyrics of "Das Lied der Deutschen" to Haydn's melody in 1841.
The song is perhaps best known for the opening words of the first stanza, "Deutschland, Deutschland uber alles" (literally, "Germany, Germany above all") which was dropped after the Nazi era.
Today, when they sing their national anthem Germans sing only the third stanza, which begins: "Unity and law and freedom for the German fatherland".