The 52-year-old coach insists he has not thought about stepping down, but hinted that he could leave his role with Die Mannschaft to seek new challenges
Die Mannschaft was widely viewed as a favorite for the title but was denied a place in Sunday's final in Kiev following a 2-1 loss to Cesare Prandelli's men.
Earlier in the month, Low gave a strong indication that he could step down as Germany coach after the 2014 World Cup, stating that change is "sometimes necessary".
However, he has come under fire following the team's failure to win the Euros, and the 52-year-old has refused to say whether he will remain in charge for the World Cup qualifiers.
"Generally, I have a contract," Low told Bild. "Leaving? Such things have not crossed our mind. Our journey has been very, very good.
"I must get a little distance to see if there are any new attractions out there."
Low took over from Jurgen Klinsmann in 2006, guiding Germany to a runner-up finish at Euro 2008 and third-place at the World Cup in South Africa, two years later.