Parma are enduring a torrid season in the league, with a record of only three wins from 20 matches leaving them bottom of the table, but the cup has provided a modicum of relief.
Roberto Donadoni's men knocked out Cagliari in the last round, but their task is much tougher in the last eight, with Serie A leaders Juventus travelling to Stadio Ennio Tardini.
Allegri will not be taking victory for granted, though, saying Juve must focus if they are to end their 20-year wait to lift the cup.
"Tomorrow's game is a quarter-final, we have an obligation and a duty to try and make the semi-finals," he said. "I believe it's 20 years since Juventus won the Coppa Italia, so this should be one of our main goals with the league and the [UEFA] Champions League.
"We must not think that we'll go to Parma tomorrow and find an easy game, because it's an important game for them too, to try and make it into a semi-final.
"It will be difficult, very difficult, so we must not underestimate the commitment that will be needed tomorrow night.
"We must approach it with the right attitude, knowing that it won't be an easy game, partly because in recent games - although they didn't get results - Parma have played well.
"Let's not forget, they've beaten Inter and Fiorentina in the league."
Juve could welcome back midfield maestro Andrea Pirlo from illness for the clash, while Andrea Barzagli is nearing a return to the first team following a foot injury.
