Milan came from two goals behind to win 3-2 in Riyadh on Monday evening.
Cardinale was not in Saudi Arabia for the final, but sent a message to Ibrahimovic, who spoke to the players on his behalf.
“Congratulations on this extraordinary result. Winning this trophy in a derby is special and something to be extremely proud of,” Cardinale told the team.
“It has been a challenging season so far, but you have to enjoy this moment and return to Italy with this boost to claim the place where Milan belongs in Serie A. I embrace you and I am with you every moment. “
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