Gattuso took over after Carlo Ancelotti was sacked despite Napoli’s 4-0 Champions League win over Genk booking their place in the last 16 in midweek.
But the former AC Milan coach’s reign got off to the worst possible start as the southerners drop to eighth — 17 points behind leaders Inter Milan who play Fiorentina on Sunday.
Gervinho struck the winner in the third minute of injury time after Dejan Kulusevski had put Parma ahead after just four minutes in Naples.
Arkadiusz Milik pulled the hosts level on 64 minutes in the game which had been delayed after high winds damaged the roofing of the San Paolo Stadium.
“I don’t believe in bad luck. Right now we’re not good mentally,” said Gattuso.
“The team is paying for the fact that it has not won (in the league) for 50 or more days.
“The first 10 minutes also prove it. It’s tough as are the whistles of the fans. There’s a lot of work to do.”
Kulusevski struck early as defender Kalidou Koulibaly lost control of the ball minutes into the game.
The Senegalese defender went off with a thigh injury just after his blunder, with Parma also losing striker Andreas Cornelius to injury after quarter of an hour.
Napoli captain Lorenzo Insigne missed chances to break through, inexplicably sending wide with just Parma goalkeeper Luigi Sepe to beat.
Gattuso brought on Dries Mertens after an hour with the Belgian setting up Milik to head past Sepe, the Polish striker following on from his hat-trick against Genk.
Gervinho threatened when he raced up the pitch, past the Napoli defence with Alex Meret stopping with his foot.
The Ivorian finally broke through three minutes into added time, scoring after a counter-attack with Kulusevski.
“Insigne? He’s not the problem, he’s not the only one who played badly,” said Gattuso as Napoli sit eight points off the Champions League places with their last win against Verona on October 19.
Parma move up to seventh.
Gattuso missed out on the Champions League places with AC Milan last season.
But the former World Cup winner with Italy, conceded Napoli’s poor run of form was inexplicable.
“That (Milan) was a team in trouble, but it came from four or five years with problems,” said Gattuso.
“Here everything that is happening is something new.
“In the dressing room are players who have written important pages of this club, with excellent results, and now they find themselves dealing with a situation they have never experienced.”
Napoli travel to Sassuolo on December 22 for their final game before the winter break.
Gattuso added: “Fourth place? More than thinking about that right now we have to work to improve ourselves and think game by game.”
Elsewhere Brescia beat Lecce 3-0 to move out of the relegation zone with just their second back-to-back win of the season.
Jhon Chancellor and Ernesto Torregrossa put Brescia ahead in a 12-minute spell before the break with Nikolas Spalek adding a third just after the hour.
Genoa host city rivals Sampdoria in a relegation battle later Saturday.
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