It was decided in a penalty shoot-out, where Mario Mandzukic hit the bar and Gianluigi Donnarumma stuck up a hand to save Paulo Dybala's spot-kick.
And Marchisio has warned his team-mates Milan - who claimed a 1-0 win win in October's Serie A clash - will be desperate to emerge victorious this time around and lift the trophy.
First, Giorgio Chiellini scored a goal any striker would have been proud of, guiding home Mirajlem Pjanic's pin-point corner to give Juventus the lead in the 18th minute.
Stefano Sturaro should have opened the scoring in the 17th minute but, after being played in by Gonzalo Higuaín, the midfielder's effort lacked power and was repelled by the Milan keeper before the ball was scrambled behind by Ignazio Abate. At that stage it was all Juventus, but they were pegged back just before half-time when Giacomo Bonaventura beautifully glanced home a Fernandez Suso cross.
Juventus also had their chances, most notably in extra time.
A "very angry" Juventus coach Massimiliano Allegri said he was upset at the way his team had lost control of the game and become nervous.
For the legendary goalie Gianluigi Buffon this match was the 600th in Juventus.
"What sets this group apart is our ability to make the most of whatever chance comes our way and take any challenge we face head on".
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