The Catalans won all seven of their opening fixtures but Flick's heavily rotated side came badly undone in Pamplona as Ante Budimir scored a brace either side of Bryan Zaragoza's strike.
Pau Victor had given Barça a lifeline to pull them back into the game before Budimir bagged his second from the penalty spot.
Abel Bretones added a sensational fourth from the edge of the box, before Lamine Yamal pulled one back with a fine effort of his own.
Victory would have matched Barcelona's best ever start to a league campaign with eight consecutive wins, but they were not able to build on their four-point lead on second-place Real Madrid.
The Spanish champions visit Atletico Madrid, third, in a derby clash on Sunday.
"In the first half we made a lot of mistakes, it's not normal we play like this -- we had a lot of changes in the team and this is maybe one reason for that," Flick told reporters.
"I think it was necessary. We had so many matches, a lot of players had so many minutes, I have to take care about that. This is my responsibility.
"If you want to blame someone for this defeat then take me."
Ahead of a Champions League match against Young Boys on Tuesday, Flick felt he had to shuffle his pack, especially after Barça lost at Monaco in their European opener.
The coach, missing several key players through injury, handed starts to inexperienced defenders Gerard Martin and Sergi Dominguez as well as Pablo Torre in midfield and Victor in attack.
The coach rested Spain Euro 2024 starlet Yamal and Brazilian winger Raphinha among other regular picks.
As a result Barcelona failed to ignite in the first half and Osasuna winger Zaragoza took centre-stage.
Last season Zaragoza struck twice while playing for Granada in a 2-2 draw against Barça, a performance which helped earn him a move to Bayern Munich.
On loan from the German giants, Zaragoza created the opener for target-man Budimir with a fine cross, which the Croatian nodded home with ease in the 18th minute after escaping the attentions of Dominguez.
Zaragoza finished the second himself 10 minutes later after being sent through on goal, with the winger bypassing goalkeeper Inaki Pena with a fine ball roll and then slotting into the empty net.
Barcelona complained there had been a foul on Victor in the build-up but the referee waved their complaints away.
The leaders created little themselves, with the best opening falling to Ferran Torres. However, the Spanish winger miscontrolled on the edge of the box and was quickly swallowed up by the Osasuna defence.
