Having conceded four goals to Sweden and the United States in the past year, it was Paraguay's turn to lay bare the deficiencies which continue to plague the Germany defence with less than a year to the start of the World Cup.
Low has refused to change his attacking system, but warned a lot of work needs to be done at the back.
"It's hard to judge this game," said Low to ZDF television.
"In the first half we made some elementary, glaring mistakes. We were too negligent in all of our defensive work, giving our opponents far too much room.
"When teams attack us early on then we must not lose our shape, which is currently one of my favourite issues.
"Sometimes we are too passive. Certainly we're not going to play like this against Austria. We will improve."
Conceding three goals is not something goalkeeper Manuel Neuer is used to, and he admits it is not something he would like to do regularly either.
"I think this was a warning at just the right time," said the Bayern Munich player. "We can't play like this against Austria.
"We've got to analyse it and correct it."
Germany host Austria in Munich on September 6 with victory in that game, and the trip to the Faroe Islands four days later, probably enough to book their ticket to next summer's World Cup.