Die Mannschaft went into the tournament as one of the favourites to win the World Cup, which would have been a second consecutive triumph.
However, after a dismal showing against Mexico when they lost 1-0 and a narrow victory against Sweden, in which Toni Kroos scored a last minute free kick, they went into their final game against South Korea expecting to win.
Sweden's victory over Mexico meant Germany needed to take all three points but two late goals from the South Koreans sent Germany packing at the group stage for the first time since 1938.
After the game, Low appeared non committal about his future, despite being handed a new contract to 2022 before the tournament started.
He said: "Where do we go from here? We'll have to go from here. It would be premature for me to say anything at this point, but we will talk calmly about it."
However, according to reports in Germany, Low will be allowed to stay in charge as they try and come back from their poor showing in Russia.
He has been manager of his country since 2006, and won the Confederations Cup last year as well as the 2014 World Cup.