Hirving Lozano hit the winning goal after 35 minutes in Moscow when the German defence was caught napping.
This was the first time Germany have lost an opening game at a World Cup finals since going down 2-1 to Algeria when Spain hosted the 1982 tournament.
Top-selling German daily Bild declared on their website: "Embarrassing performance against Mexico: this crash causes us World Cup worry".
Munich-based newspaper Sueddeutsche Zeitung agreed with "There are reasons to worry" over a picture of the dejected German team, who need to beat Sweden and South Korea to be sure of going through.
The Frankfurter Allgemeine newspaper went for "Fiesta Mexicana: False start for Germany".
Magazine Sports Bild commented "There were no world champions to be seen on the pitch" in a damning verdict on the below-par performance.