The Giallorossi were on level terms at half-time on Sunday after Diego Perotti's penalty cancelled out Arkadiusz Milik's second-minute opener for Napoli.
But goals from Dries Mertens, Simone Verdi and substitute Amin Younes condemned Roma to a fourth defeat in five games across all competitions.
Head coach Claudio Ranieri began with a victory over Empoli following his arrival on March 8, but since then he has suffered back-to-back defeats against SPAL and Napoli, and Pallotta pulled no punches in his assessment of the club's predicament.
"Everyone knows what's gone wrong this season, that's why we had to make changes", Pallotta told the club's official website.
Roma face Fiorentina at Stadio Olimpico tomorrow ahead of a trip to Sampdoria, with seventh-placed rivals Lazio just behind them in the Serie A table.
"No more alibis for anyone, players have to stand up and show they have balls" said Pallotta.