Empoli, who are battling relegation, opened the scoring after four minutes when striker Alberto Cerri headed in a close-range cross for what proved to be the winner.
"We're not mathematically out of it but the chances of us getting there are very slim," said Calzona after his first league defeat as Napoli boss
Italian club Napoli said they were "stunned" after Italy's football federation (FIGC) on Tuesday dropped a probe into alleged racist comments made by Inter Milan's Francesco Acerbi to Napoli's Juan Jesus due to lack of evidence.
Barcelona came flying out of the blocks with goals from Fermin Lopez and Joao Cancelo but after Amir Rrahmani pulled one back, the Catalans started to sweat.
Nigeria forward Osimhen rolled home the leveller with 15 minutes left of the first leg of their Champions League last 16 tie at the Stadio Diego Armando Maradona, in his first match since returning from the Africa Cup of Nations.
The 62-year-old Mazzarri became the second man to be sent packing this season by the ailing Italian champions.
Nigeria striker Victor Osimhen will leave Napoli this summer and join "either Real Madrid, Paris Saint-Germain or an English club", the Italian club's president and owner Aurelio De Laurentiis said on Friday.
Napoli put aside their recent troubles on Thursday by reaching the Italian Super Cup final with a convincing 3-0 win over Fiorentina in Riyadh.
Napoli striker Victor Osimhen has replied angrily to suggestions that he would leave the Serie A side for Saudi Arabia at the end of this season from agent Mamuka Jugeli, who represents club team mate Khvicha Kvaratskhelia.
Thousands of joyous Napoli supporters greeted the team early Monday as they returned from their victory over Juventus, which brought the prospect of a historic Serie A title within touching distance.
Giacomo Raspadori smashed in the stoppage time decider to claim a huge win at Juve which pushed Napoli 17 points clear at the top of the table, sweeping aside disappointment at being knocked out of the Champions League by AC Milan midweek.
Leaders Napoli were held to a goalless home draw by relegation-threatened Hellas Verona in Serie A on Saturday as Luciano Spalletti's side finished winless for the third time in their last four games in all competitions.
Ismael Bennacer gave AC Milan a slim advantage in their all-Italian Champions League quarterfinal against Napoli with the only goal in Wednesday's tight 1-0 first-leg win.
Napoli took another step closer to ending their 33-year wait to win the Serie A title after they came away from Lecce with a 2-1 win on Friday thanks to a bizarre own goal from Lecce defender Antonino Gallo.
Juventus have been ordered to close part of their stadium for their next home Serie A match against Napoli by an Italian sports judge after Inter Milan striker Romelu Lukaku was racially abused during Tuesday's Coppa Italia semi-final.
Milan have 51 points, one ahead of fourth-placed Inter Milan, and are four behind second-placed Lazio. Napoli are 20 points clear at the top
The face of a young Diego Armando Maradona gazes down from a mural in Naples' Miracles Square, watching the city gear up for a celebration it hasn't enjoyed since the Argentine soccer star was at his peak more than 30 years ago.
While the fans of Italian football continue to struggle to convince their peers from the English Premier League and LaLiga about the relevance of Serie A in European footballing hierarchy, it is with a renewed optimism that they can now boast about Napoli – the new entertainers of European football.
Serie A leaders Napoli thrashed Torino 4-0 away with a double from Victor Oshimen and goals from Khvicha Kvaratskhelia and Tanguy Ndombele on Sunday to move closer to the title.