"When you lose a game, you are annoyed, but I am more annoyed about the manner in which we lost," said Löw.
But while he felt the team never found their game, French coach Laurent Blanc hailed his side's disciplined display after scoring an early goal against Germany.
Germany were missing five stars in captain Philipp Lahm, his deputy Bastian Schweinsteiger, midfielders Mario Götze and Lukas Podolski, plus defender Per Mertesacker with injury - and their replacements failed to cope with the French.
It was Brazil-born striker Cacau who scored the team's only goal, which came late in the game.
Löw had repeatedly stated the result would not rattle German confidence in their quest to win a fourth European title in Poland and the Ukraine this June, but the lack of discipline in defence was a concern.
"We were fairly solid in the first half, but we lost our rhythm in the second and the French got stronger as the game wore on."
"We have achieved a lot and progressed as a group, but this result shows we still have things to work on."
Bayern Munich midfielder Thomas Müller hinted at disharmony in the ranks as the German defence was badly exposed on occasion.
"After such a performance, you can't really say a lot," he said.
In contrast to Germany, France were pragmatic and took their chances as their attack found plenty of space to exploit in the hosts' defence.
Blanc said he took great pleasure in watching the match, but that they had identified weaknesses in Germany's defence.
After the debacle at the last World Cup, France are showing signs of returning to form with a trio of friendlies still to come before the Euro.
Germany will be hoping for a more composed performance when they take on Switzerland in Basel on May 26 then Israel in Leipzig on June 1.
"We have been criticised for not playing as a team, but tonight we showed remarkable team spirit. This narrows things down for Euro places," said Blanc.