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.
Spalletti has just led Napoli to the Serie A title for the first time since 1990 but there has been speculation about whether he would stay on.
The 24-year-old is now the highest scoring African player in the history of Serie A after overtaking George Weah and lapped up the applause of Napoli fans as the team did their post-match lap of honour
Napoli's champions returned home Friday after winning their first Serie A title in 33 years, greeted at their training camp by hundreds of jubilant fans following a raucous night of partying in Naples.
More than 200 people ended up in hospital overnight for injuries sustained during the celebrations, La Stampa said, from knife wounds to burns from firecrackers and asthma attacks caused by inhaling smoke from flares.
Retired midfielder Alemao, who won Serie A with Napoli in 1990 alongside late legend Diego Maradona, says he regrets his friend is not alive to celebrate the team's return to glory 33 years later.
Victor Osimhen said Thursday that he will never forget winning Napoli's first Serie A title in over three decades after his goal finally pushed southern Italy's biggest club over the line.
Napoli will have to wait at least one more day to be crowned Italian champions after Lazio beat Sassuolo 2-0 on Wednesday to reclaim second place in Serie A.
Leaders Napoli were held to a 1-1 home draw by Salernitana in Serie A on Sunday, extending the wait of Luciano Spalletti's side to seal their first title in 33 years.
Inter Milan came from a goal down to win 3-1 at home against Lazio in Serie A on Sunday, giving Napoli the opportunity to seal their first title since the Diego Maradona era this weekend.
In order to win the league a record-breaking six matches before the end of the season, Napoli have to hope closest challengers Lazio do not to win at Inter Milan in Sunday's early kick-off