"It's very, very hard to put it into words", said Germany defender Mats Hummels, a member of the team that won in Brazil four years ago.
Germany, the winners of the last World Cup in 2014, opened up their campaign in Russian Federation with a narrow 1-0 defeat to Mexico.
"I think the problem is the famous fifth match", he said, adding that Mexico felt more comfortable as underdogs.
Germany ended up last in Group F while Sweden and Mexico advanced to the round of 16.
"It's a dark day for German football", Germany goalkeeper Manuel Neuer said.
The article on the official website had listed five reasons for Germany's group-stage exit.
Cilantro's Mexican Restaurant is giving customers of Korean descent a 25 percent discount Wednesday after the South Korean national soccer team's World Cup victory propelled Mexico into the Round of 16 that morning.
The DFB extended Loew's contract as Germany head coach until 2022 just before the World Cup kicked off, and Grindel had previously stated Loew's job was safe regardless of how Germany perform at the tournament.
"We believe there will be a transition that will take place after the World Cup, regardless of the outcome of the tournament, and no one is better equipped to handle that than Jogi Low", said German F.A. President Reinhard Grindel, per ESPN. "Twenty-two men chase a ball for 90 minutes and at the end, the Germans always win".
One former Mexico coach, Ricardo La Volpe, suggested that the players were already feeling the weight of the so-called "fifth match" - the elusive quarter-final - as they fell apart against the physical Europeans.
Fellow supporter Denis, who traveled nearly 3,000km (1,864 miles) from his home in Stuttgart to watch Germany take on South Korea in Kazan, was equally resigned.
"We should not be doing things for the sake of things now, but rather get on the way the far-reaching changes we need now", Grindel said.