The 6-0 drubbing in Seville on Tuesday was Germany's heaviest defeat for 89 years as Spain completely dominated the Nations League match in Seville.
The Bild daily was blunt in its assessment, headlining its coverage: "Loew should offer to resign."
"Just seven months before the Euro, the German FA has to answer the question whether Joachim Loew is still the right man for the tournament," the paper said.
Ferran Torres scored a brilliant hat-trick as Spain attacked at will with Loew's Germany side offering little resistance as they slumped to their heaviest defeat since losing 6-0 in Berlin against Austria in 1931.
Loew batted off questions about his future in the post-match press conference.
"You have to ask others. I can't answer that spontaneously," he replied when asked if he was worried about his job.
Loew led Germany to the 2014 World Cup but the credit from that triumph was largely dissipated by the debacle at the 2018 finals in Russia when Germany crashed out in the group phase.
Loew's contract with the German federation runs until the 2022 World Cup and he appears to still have the support of Germany team director Oliver Bierhoff.
"The confidence is completely there," Bierhoff insisted in the wake of the drubbing, but promised a "hard analysis".
Bierhoff pointed to a lineup on Tuesday containing veteran players Manuel Neuer, Ilkay Gundogan and Toni Kroos as proof that "lack of experience of the players is no excuse".
Bastian Schweinsteiger, who won the 2014 World Cup under Loew, was horrified by the performance.
"It did not feel like a team - there were no commands" in the German ranks, said the 36-year-old, who now works as a media pundit.
"You only heard the Spanish talking. You have to change something. The German national team can't play like that.
"There are certain values, which I didn't see on the pitch."
Munich-based newspaper Sueddeutsche Zeitung said the humiliation in Spain must fuel the debate "How much longer with Jogi Loew?".
"The fiasco in Seville will obviously have consequences," said Cologne-based Express. "Is Joachim Loew still the right coach for the national team?"
Schweinsteiger reignited the debate about whether three other veteran players who Loew has sidelined from the national team -- Mats Hummels and Bayern Munich's Champions League-winning pair Jerome Boateng and Thomas Mueller -- should be reinstated.
Loew told all three in 2019 that their Germany careers were over, yet the trio are all currently in great form for their clubs.
"This is the German team, it has to bring together the best players," Schweinsteiger said, adding that Mueller and Boateng would be in his team for Euro 2020 if he were coach.
"The coach has his own opinion on this, I have a different one," he added.
Even Neuer, the team's captain and goalkeeper whose record 96th international appearance was one he will want to forget, hinted the trio should return.
"I do not want to highlight any of the three named: all players could help us in principle, they have proven that often enough," Neuer told Sport Bild magazine.
Time is running out for Loew to prove he can turn things around before the Euro 2020 finals, postponed from last year, kick off in June.
"The path that the national coach has taken, I will follow up to and including the European Championship," Bierhoff told the Frankfurt newspaper FAZ.