The 2010 Champions League winners are eighth in the table on 52 points, two adrift of Sampdoria who occupy the last Europa League preliminary round spot for next season with three games left to play.
Inter have not lost in seven matches but have struggled at home recently, winning one of their last six games.
"It's our last opportunity in a do-or-die match," Mancini told a news conference on Friday.
"It's true we've had trouble at home. We're more at ease away, more relaxed, while our opponents leave us few openings when they come to the San Siro."
Mancini, who took over from Walter Mazzarri in November, rued the amount of points his side had dropped this season.
"We lost so many points we shouldn't have, against Cesena, Parma, Udinese, Sampdoria, too many," he said.
"I still believe it was a positive season as the team has improved but I thought we'd be higher in the table at this point."
Juve coach Massimiliano Allegri said on Friday that Andrea Pirlo, Gianluigi Buffon, Patrice Evra, Arturo Vidal and Carlos Tevez would not travel to Milan.
The five players will rest ahead of the Italian Cup final against Lazio in Rome on Wednesday.
(Editing by Tony Jimenez)
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