Germany were a shadow of their all-conquering self with the Mexicans springing a trap and the 2014 World Cup winners were caught on the break throughout the game.
Loew said while he was not planning to overhaul his plans for the remaining Group F matches against Sweden and South Korea, his team would bounce back.
"We will draw our lessons from this defeat and will do it better next time," the 58-year-old said. "We will certainly not throw our plans overboard. We will not deviate from our path, we just have to find our strengths again."
"It is an unusual situation for us but one we must accept. We did not play our usual offensive and passing game," Loew said.
"We will analyse it. The team has enough experience to deal with it and we will rise again."
The Germans have a stellar tournament record under Loew, having reached at least the semi-finals in every World Cup or Euro tournament since he took over in 2006.
They have also not been eliminated at a World Cup group stage since 1938 when the tournament had a different and smaller format. Since then Germany have managed to qualify for the knockout stage or the second group stage, as was the case in 1978, every time.
They next take on Sweden before facing South Korea and they must win both if they are to make sure of a spot in the knockout stage.
"One thing I will not be doing is think about the round of 16. What we need to do now is do our homework and win our next game. We are under pressure.
"It will not happen to us," he said when asked whether Germany would fall in the group stage. "We will make it."