A 1-0 home defeat to Palermo relegated Cagliari to Italy’s Serie B on Sunday as Genoa and Torino recorded valuable wins to maintain their hopes of qualifying for the Europa League.

With Juventus crowned champions a fortnight ago and the fight for Champions League places ongoing between Lazio, Roma and Napoli, Sunday’s early fixtures held mixed fortunes for Serie A’s also-rans.

A 2-1 home defeat to Juventus on Saturday damaged Inter Milan’s chances of qualifying for the Europa League and Roberto Mancini’s men remain eighth, now three points behind sixth-placed Fiorentina.

Across the city, nerves are jangling just as much with the distinct possibility of neither Milan side making it into Europe next season.

A hat-trick from Sassuolo striker Domenico Berardi in a 3-2 home win over AC Milan ended the slim chances the seven-time European champions’ had of Europa League qualification.

Milan coach Filippo Inzaghi’s future with the club remains uncertain, but after complaining Sassuolo’s opener “was not valid”, the former Rossoneri striker launched a plea for a stay of execution.

“I have a contract with Milan and feel honoured to be here,” he said.

“Sassuolo wanted me when I was Milan’s youth coach, but I am too close to Milan and I hope to stay because I still have so much to offer.”

But Milan were not the only side holding their heads in disappointment.

Cagliari started the day knowing anything less than a win would prove fatal and the Sardinians were a goal down after just nine minutes when Franco Vazquez struck for the Sicilians, who held on to their 1-0 lead to move up to 10th place.

Cagliari have now joined Cesena and Parma in Serie B a day after Frosinone, a club based 50 kilometres south of Rome, joined Carpi in grabbing one of three promotion places to Italy’s top flight.

Among the day’s biggest winners were Genoa and Torino, both of whom remain in contention for a Europa League place although the latter’s chances appear slim.

Hosts Atalanta took an 18th-minute lead from the spot against Genoa thanks to Mauricio Pinilla, but the Bergamo-based side were stunned by four goals from the visitors including a brace from Iago Falque.

Genoa’s 4-1 win moved them up to fifth place, one point ahead of Fiorentina, and pushed city rivals Sampdoria down to seventh and out of the Europa League reckoning following their 1-0 loss at home to Lazio on Saturday.

A brace by Maxi Lopez handed Torino a precious 2-0 home win over Chievo that left the Granate in ninth place but now only four behind Fiorentina.

If Fiorentina slip up against Parma on Monday, Sampdoria, Inter and Torino — with only three points separating the sides — will see their European chances given a boost.

“We don’t have any intention of giving up our chase for Europe, or for anything else,” said Torino’s Argentinian striker Lopez.

“It’s only normal you give it everything for the club, especially in front of the fans.”

Roma host Udinese in Sunday’s late game looking to restore their one-point lead on Lazio as the city rivals battle for the second automatic Champions League qualifying spot.

Napoli, four points behind Roma in fourth, host Cesena on Monday looking for the win that would seal European qualification as well as maintain their hopes of catching the capital sides over the closing two games