Roberto Mancini's men are languishing in 10th after a winless run of four saw them enter the international break on a sour note.
A club of Inter's stature should be challenging for the title, not scrapping in mid-table, and their plight is underlined by the fact 16th-placed Verona are just five points behind them.
A home clash against rock-bottom Parma - who have collected just nine points this season amidst significant financial toil - should see Inter return to winning ways, though.
Inter can ill-afford another slip-up as they are 10 points behind Napoli, who occupy the final European spot in fifth.
And Jesus said his team-mates are still desperate to play continental football, with the knowledge that their holidays could be cut short if they fail.
"We have to deal with these remaining games as if our lives depended on it," he told Sky Sport Italia.
"If we're not able to get into Europe for next season then we'll be at the club's disposal if they want to shorten the holidays.
"The break has done us good…we've been able to rest mentally and training with conviction.
"The club is doing everything it can to take Inter back up where it belongs next season.
"We need our fans support on Saturday and I know they'll help us out."
Inter have been linked with a big-money move for Manchester City midfielder Yaya Toure this week.
Their last league win came in February, at Cagliari, also in the relegation zone.
You have to go back to mid-January to find Parma's last win in any competition - a Coppa Italia success, against Cagliari as well.
They shocked Fiorentina in January too, but with their relegation to be confirmed in the coming weeks, bar a minor miracle, another upset is unlikely.
Parma's defence is the equal-worst in the league, having conceded 53 times, and while Inter have battled this term, they are still the fourth-highest scorers in the league.
Argentinean forward Mauro Icardi has netted 15 Serie A strikes this term, with only Juventus marksman Carlos Tevez (16) having scored more.
Antonio Cassano, who left Inter to join Parma last year, is top scorer for the strugglers with five.
Parma did beat Inter earlier this season, 2-0, thanks to Paolo De Ceglie's double.
But they have a terrible record against Inter at San Siro, last winning in May 1999. In the 17 games since, Inter have won 11.
