The Elefanti have slipped to eighth courtesy of three defeats from their last four games, leaving their ambitions of securing a first-ever Europa League campaign hanging by a thread.
Fifth-placed Inter Milan are only five points away, though, and with eight games left to play Rolando Maran's men could still achieve their lofty target, starting with victory over homeless Cagliari.
Bergessio told the Corriere dello Sport: "Sunday is the last train for Europe. We will have to fight right to the very end to achieve our goal.
"Unfortunately the last few results have complicated our plans and now we have to pick ourselves up again and forge our own destiny in the league.
"We need to do the best we possibly can from game to game.
"Cagliari are a tricky team and a strong one. It will be a tough game for us and I hope the fans are behind us because that always gives you an extra boost."
Blazej Augustyn, Ciro Capuano and Fabio Sciacca are injured and join suspended striker Pablo Barrientos on the sidelines against Cagliari, who are facing an uncertain future following this week's developments.
In a turn of events that mirror the stadium crisis of the 2011-12 season, the Sardinians are looking for a new venue for their four remaining home games after deciding to abandon the controversial Stadio Is Arenas.
Ongoing safety concerns at the new build in Quartu Sant'Elena forced a string of games to be played behind closed doors and with appeals consistently falling on deaf ears, Cagliari informed local authorities they would be cancelling their contract and moving on.
A return to the Stadio Nereo Rocco in Trieste - where the Rossoblu closed out last year's fixtures - is a possibility, despite the Slovenian border city being over 600 miles away.
Defender Nicola Murru and midfielder Andrea Cossu are suspended for the trip across the Tyrrhenian Sea, from which Cagliari claimed a 1-0 win last season before the points were shared from November's goalless draw in Sardinia.