Current holders, Germany begin defence of their World Cup title this Sunday when they take on Mexico.
Juan Carlos Osorio's side had other ideas, however, holding their own against the favourites' fearsome but slowing midfield and finding space at the back and seeking to end 33 years without a win against Germany.
Die Mannschaft improved in the second half and applied pressure on Mexico, but the Central Americans held out at the Luzhniki Stadium to condemn Germany to their first World Cup opening-day loss since 1982.
Hirving Lozano's winning goal against Germany sparked wild celebrations in Mexico.
"We will certainly not change our match plan", he said.
Kroos, who like Hummels was part of the team that won the 2014 World Cup, said Germany paid the price for failing to stem the waves of Mexican first-half attacks.
Germany coach Joachim Loew did not mince his words, saying: "We played very badly".
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Mexico got its deserved lead in the 35th minute.
And when Rafael Marquez came on in the 74th minute he made history too, tying a record by playing in his fifth World Cup.
"We always thought of having two quick players on the wing", Osorio said in his post-match press conference.
"We did not find any solutions to their game in the first half", the Real Madrid player told German broadcaster ZDF. Chicharito played Hirving Lozano into the box on the left channel, and the PSV winger looked to have a clear close-range look until Jerome Boateng came up with a well-timed slide tackle to block the chance.
He said: "We played with bravery when it was needed and defended with all our hearts, I think we need to give the credit where it's due and that's to the players".
Check out our brand new daily JOE World Cup Minipod with Dion Fanning and Paddy McKenna with added Mad Vlad Putin, Spanish managerial weeping and probably some football as well.
Germany trailed only once in the last World Cup, 2-1 to Ghana, and has outscored opponents 20-2 in its past four World Cup openers.
Low was at a loss to explain his side's lacklustre display but backed them to put it right in their remaining Group F fixtures against Sweden and Korea Republic.
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