Germany, meanwhile, had 26 shots without causing Guillermo Ochoa too many problems, although the Mexico goalkeeper made nine saves in keeping a memorable clean sheet.
Hummels felt Germany did not heed the warning of their final warm-up friendly against Saudi Arabia that ended in a tight 2-1 win, their only success in seven matches since the end of the World Cup qualifying campaign last year.
"It's pretty simple. We played like we did against Saudi Arabia, but against a better opponent," Hummels said to ZDF.
"We talked about a few things, such as not losing possession and protection, which unfortunately we did not put into action today.
"Mexico deserved the game because we made it too easy for them, knowing we should not have allowed that to happen.
"If seven or eight players play offensively, then it's clear that the offensive force is greater than the defensive stability. That's what I often say internally.
"Our stability is not good, you have to say - often only Jerome [Boateng] and I were at the back, so they mercilessly attacked us."
"A wake-up call is too late, we now have to win two games, otherwise the World Cup is over," Hummels said. "We actually had the wake-up call against Saudi Arabia."
1 - Opening game at the World Cup for reigning champions in the 21st century:— OptaJean (@OptaJean) June 17, 2018
2002 France 0-1
2006 Brasil 1-0
2010 Italy 1-1
2014 Spain 1-5
2018 Germany 0-1
Pressure. #GERMEX #WorldCup pic.twitter.com/8g3kXZHSwA
Real Madrid midfielder Toni Kroos joined Hummels in demanding an improved performance when Germany take on South Korea on Wednesday in Kazan.
"I think we did not find any solutions in the first half," Kroos said.
"Mexico were clever, we did better in the second half and Mexico got tired.
"We're under pressure now, without question, we have to get six points from the two games, if possible."