An extra-time goal from Patrick Cutrone secured a 1-0 win at San Siro on Wednesday and sent Milan into the semi-finals, where they will meet Lazio.
The win gave Rossoneri fans something to celebrate during another difficult season, with their side having lost their last two Serie A games without scoring a goal to find themselves 11th in the table.
But Gattuso says one result will not change everything for the club ahead of a tricky visit to Fiorentina on Saturday.
"I'm no magician," he told a news conference. "It was a very difficult game but we need to take things one match at a time. We need to keep working and showing the attitude I've seen during this period.
"We want to finish this first half of the season in a better way. We know the problems we had and that we still have.
"It was an important match and it's given us a lot of strength. Now we're playing a Fiorentina side in very good form and we go into it with a lot of fatigue."
Here's the 23-man squad that will travel to Florence for #FiorentinaMilan https://t.co/qvlli0HT5e— AC Milan (@acmilan) December 29, 2017
Mister Gattuso ha convocato 23 rossoneri per la trasferta di Firenze https://t.co/R4N7V43HSg pic.twitter.com/MyfyJh0Odp
"I'd sign up for that 1000 times," said Gattuso. "I wish him massive luck. I had a great relationship with him over those few months. I have huge respect for him as a man and as a coach."