A frenetic 2-1 victory at Parma - decided by first-half goals from Francesco Lodi and Keko - saw Catania close to within two points of fifth-placed Inter with a haul of 16 points from the last 21 available.
Bergessio told newspaper La Repubblica: "We know we are in direct conflict with Inter and it will be an incredibly important match.
"All the teams in the top eight will compete for a European place, right until the very end.
"We are meeting a team who are on a very high level and we will need to concentrate for the whole match, otherwise we can't even think about winning it."
Catania may be the revelation of the season but Bergessio knows there will be a bumper crowd at the Stadio Angelo Massimino because the former European champions are in town.
"We are expecting a full stadium and we feel good when our fans are close to us, which is important," he added. "Home games usually finish in our favour and that has to mean something."
Head coach Rolando Maran has a few personnel concerns, though, with suspended defenders Nicola Legrottaglie and Giuseppe Bellusci joining the injured quartet of Fabio Sciacca, Ciro Capuano, Pablo Barrientos and Sergio Almiron on the sidelines.
Suspended Inter defender Andrea Ranocchia will not have to play through the pain of a knee injury for a second week running as the Milanese giants travel to east Sicily.
It has been a bittersweet week for Inter, who were hit with a fine from the Lega Serie A following the unsavoury events of Sunday's Milan derby.
Relief spread around the blue half of the San Siro when Ezequiel Schelotto headed an equaliser to deny AC Milan all three points, after Stephan El Shaarawy had opened the scoring, but several Inter fans had been observed racially abusing Rossoneri striker Mario Balotelli.
Ranocchia told inter.it: "I tried to grit my teeth and the medical staff did a fantastic job to get me out on the pitch for the derby.
"We responded superbly after going behind and we ended on a high. That gives us a boost going into the next game."
Inter are one of six teams who have a realistic chance of securing third place and Champions League football, and Ranocchia sees tomorrow's game as a potential obstacle to success.
"It's a pretty intense battle and it makes it very intriguing," he added. "It's been a hard-fought Serie A this year but we'll keep fighting until the end because we must get into the Champions League spots."
Matias Silvestre, Walter Samuel, Joel Obi, Luca Castellazzi, Gaby Mudingayi, Diego Milito and Yuto Nagatomo are all nursing injuries and are unlikely to travel.