The triple World Cup winners are on track to qualify for the 2014 finals in Brazil next year and are desperate to build a team that will end a title drought stretching back to 1996.
But Wednesday's defensive display against the bottom team in the World Cup South America qualifying group disappointed the fans in Kaiserslautern.
"It is always difficult to prepare for an international game with just two training sessions," skipper Philipp Lahm told reporters.
"The players came from different clubs with different systems, you need time to find your game. Next time we will be together for five days and that is good time to prepare for a qualifier."
Coach Joachim Loew said: "You could see some players were lacking freshness", referring to the rigorous pre-season training camps the squad have gone through with their club sides.
The Germans found themselves trailing 2-0 after 13 minutes with central defenders Per Mertesacker and Mats Hummels repeatedly exposed by the speedy Paraguayans.
It was only after the introduction of centre half Jerome Boateng in the second period that the home team managed to keep their opponents quiet.
"We know that defensively it did not work. It was clearly our mistakes that led to the goals," said midfielder Thomas Mueller.
Germany have now conceded 10 goals in six internationals this year. Wednesday's game was also the first time since 1964 that they have conceded two or more goals in two consecutive games, after losing 4-3 to the United States in June.
In 12 matches since reaching the Euro 2012 semi-finals, Loew's men have managed only three clean sheets.
"This will not continue because we will definitely stabilise," said the coach of Germany's overall performance. "We will show the team and the individual players the mistakes and use our training to highlight them.
"We made elementary mistakes but I am convinced each player will be much improved come September."
Germany, top of World Cup Group C qualifying with 16 points from six games, host Austria on Sept. 6 before travelling to the Faroe Islands four days later.