Milan find themselves languishing in 11th place in Serie A after 18 games, the Rossoneri having suffered back-to-back league defeats before Christmas.
Gattuso only replaced Vincenzo Montella last month, but the change has yet to bring about a revival, with the former youth coach having only won twice in six games in all competitions.
Last weekend's 2-0 reverse against Atalanta was the latest setback, but a last-eight cup clash with Inter provides an opportunity to heal some wounds.
Gattuso – who has rejected rumours he will walk away from the job – knows the importance of beating Inter in any competition, but with the chance to win silverware so close it brings added significance.
"The Milan derby is a very tough match but we need to try and win this game," he told Milan TV.
"It's like playing the World Cup final for us. Tomorrow's game can change our season.
"We have to reset everything.
"We'll be playing as the home side and want to bring back the enthusiasm in our fans, we owe them this.
"We need really great desire. Each and every one of us has to give something more."
Inter won October's league meeting between the two, Mauro Icardi's hat-trick securing a 3-2 victory.