AC Milan matchwinner Patrick Cutrone believes his extra-time goal against Inter in the Coppa Italia quarter-final will give his struggling side a much-needed morale boost.

The teenager came off the bench to settle the tie, scoring after 104 goalless minutes at the San Siro on Wednesday to set up a semi-final meeting with Lazio.

Milan had lost three of their last five matches in all competitions, as well as their last derby meeting with Inter, leading head coach Gennaro Gattuso to compare the clash to a World Cup final.

And 19-year-old Cutrone came up trumps by turning in Suso's perfect pass to send the Rossoneri supporters wild, the academy product celebrating deliriously in front of his home fans.

"To think that yesterday I was in the Primavera youth team and I celebrated like that after scoring in the derby, to score in front of this crowd is just incredible," a disbelieving Cutrone told Rai Sport.

"I think we needed this victory for morale. The derby can never be described as a normal game.

"Now we relish this victory and passage to the next round, then tomorrow we'll start preparing for [Saturday's league game at] Fiorentina."

Milan are eight places below Inter in the Serie A table and had to start their third-choice goalkeeper Antonio Donnarumma, as his younger brother Gianluigi was ruled out with a groin problem and Marco Storari was injured in the warm-up, having been set to deputise.

But Donnarumma made a string of saves to recover from a nervy start, blocking Joao Mario's close-range shot and allowing Cutrone to come up with the matchwinner.

And the teenager, Milan's top goalscorer with nine goals in all competitions despite the club's heavy spending in the transfer market, said his desire to make the difference was key.

"My dream is to stay here as I love Milan and I want to remain with this team," Cutrone added.

"My movement on the field is dictated by my hunger and determination. I came off the bench and really wanted to score a goal.

"I dedicate it to my family, as they always supported me. Any goal I score in future will always be dedicated to them."