The result is likely to fuel speculation that coach Antoine Kombouare is about to lose his job, although PSG still lead the standings with 30 points from 14 games, after a second-half goal by Jean Calve gave Nancy all three points.
General manager Leonardo, who left the stands minutes before the final whistle, said Kombouare's position was not threatened however.
"There is no problem," he told reporters. "Antoine has the trust of the club, even if there is room for improvement. There always is."
"The situation has not changed; He is the PSG coach."
PSG, who had not lost in Ligue 1 since their first outing of the season on August 6, lead second-placed Montpellier, 1-0 winners against Olympique Marseille on Saturday, on goal difference.
Champions Lille, who drew 0-0 at Toulouse on Friday, lie third and five points off the pace.
"It's hard to take. We're not proud. We had to win this game," PSG midfielder Nene told French TV channel Canal Plus.
"We tried everything, but we need to score," he added, referring to PSG's 24 attempts.
Elsewhere, Stade Brest beat 10-man Sochaux 2-0 while Valenciennes came from behind to beat AJ Auxerre 2-1.
At their Parc des Princes, PSG enjoyed possession and Brazilian Nene was the most dangerous player, proving a constant threat to the Nancy defence but the home side failed to create clear chances.
Nancy looked dangerous on the break and came close early on when fullback Reynald Lemaitre's attempt from just inside the box was parried away by Salvatore Sirigu.
The visitors took the lead four minutes into the second half when right-back Calve curled the ball from the edge of the box into the far top corner.
Sirigu spectacularly tipped over his bar a Calve header in the 68th as PSG, with Javier Pastore looking a pale shadow of his brilliant self, continued to struggle.
Kombouare replaced fullback Ceara with Turkey striker Mevlut Erding to try and salvage a draw at least.
PSG were transformed, piling on the pressure but Nancy keeper Guy-Roland Ndy Assembe denied Gameiro and Mathieu Bodmer from close range with quick-lightning saves with 10 minutes remaining.
