The world champions struggled to cope with the intensity of Mexico in the opening 45 minutes, and were outplayed by the North American side.
Juan Carlos Osorio's men could have doubled their lead in the 57th minute but poor decision making in the final third let them down.
It was a just reward for their positive play before the goal.
Mexico's next opponent is South Korea.
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However, Fabregas was keen to note: "We [Spain] won the World Cup and lost the first game to Switzerland, so anything can happen". I think that his skills and the professional way he plays mean that he will be the one who decides until when he wants to play.
The defeat for Die Mannschaft is their first in eight opening games at the tournament, while El Tri remain unbeaten in their six opening fixtures.
Mexico has only ever beaten Germany once in 11 tries and that win came way back in 1985.
The game started like a title fight, with both sides trading body blows in a manic first half.
The half ended 1-0 in favour of Mexico. Sometimes the criticism has been unfair, and there's no doubting the player's ability. Maybe it was meant to fire up the German team.
Mexico arguably provided a blueprint on how to beat Germany, and they could have won by more if they had taken their chances. They prepared well and hopefully they can make it. Only two teams prior, Italy in 1938 and Brazil in 1962 had managed to do it. "Teams develop and change, players finish their careers and you must bring in new players which makes it the most hard achievement". He flopped to the ground looking for fouls and dropped deeper and deeper to try get on the ball. Timo Werner collected a Joshua Kimmich cross from the right, turned and shot but his attempt was tame and straight at Guillermo Ochoa.
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Former England manager Sam Allardyce has admitted to being "jealous" of Gareth Southgate as the national side prepare for their World Cup campaign.
"They were clever and left room where they could afford to".
Joachim Low has changed the earlier style of German football of playing long balls into a more possessional style of play.
Youngster Julian Brandt almost saved Loew's night after taking over from Werner in the final minutes when he blasted a shot past Ochoa's right post, and even goalkeeper Neuer came up for a corner in injury time. The Germany manager is said to be unhappy with his decision to meet with Turkey president Recep Tayyip Erdoğan, and Ozil also has more competition for places in the German team than in recent years.
Loew, who has been in charge since 2006 and recently signed a contract extension to 2022, also raised eyebrows a few weeks ago when he did not include Leroy Sane, the English Premier League's young player of the year, in his final World Cup squad. It wouldn't be a surprise to see Ozil drop to the bench and the time has probably come for him to be dropped.
Meanwhile, Germany, the only team to have made it made it to the second round of every World Cup since 1954, needs at least a tie against Sweden on Saturday to keep that streak from ending.
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Abe told reporters that Trump had clearly conveyed Japan's stance on the abduction issue to the North Korean leader. Ordinary North Koreans consistently voice unequivocal support for the leadership when speaking to foreign media.