"I think it is awkward to make the accusation that, if the players do not sing the national anthem, they are not good Germans," Low told reporters.
"It's good to sing the anthem but it doesn't prove that the player has quality and [if he doesn't] it's certainly not a sign that he is not ready to give everything."
"We are all proud of the great things this team does and has done for integration in Germany."
Low said he was also unhappy at some of the criticism which had been aimed at his team following their shock semi-final defeat by Italy at Euro 2012.
"I can accept the sporting criticisms, with humility, and try to learn the lessons. But some of the criticisms I do not see as being purposeful," said Loew ahead of Wednesday's friendly against Argentina.
"We have a long-term concept and we are sticking by that. Before the game against Italy, we had won 15 matches in a row which is a world best. We will stay on the same path with some small corrections."
"After the World Cup in South Africa, we wanted to form a team that can win titles. Because of that, the defeat against Italy was especially painful. Now we have the job to work on our mistakes, recognise mistakes and find solutions in the next two years.
"We only had one complete week with the whole squad before this tournament," added Low after players from Bayern Munich joined the squad later than planned because of the Champions League final.
"Some of the things which we had planned could only be partly done or not at all, because we did not have enough players."
Low added that he was including 34-year-old forward Miroslav Klose in his plans for the 2014 World Cup in Brazil.
"I don't see any age limit for him," Low told reporters. "If Miro is in good physical shape, he is one of the world's best strikers, I will plan with him over the next two years."
The 34-year-old Lazio striker, who has scored 64 goals in 121 internationals, said he intended to make Brazil his fourth and final World Cup.
"If I remain healthy and keep performing, I would like to end my national team career at the 2014 World Cup," Klose told Sport Bild magazine.
Low's comments appear to contradict the policy towards Hoffenheim goalkeeper Tim Wiese, who was excluded from the squad last week at the age of 30 with goalkeeping coach Andreas Kopke saying he was looking at younger players.
"Wiese's club coach Markus Babbel reacted angrily but Low said: "Nobody has said that he is excluded for ever."
