"An incredible night," Cardinale said after the match.
"Every three days we play a game, overcoming injuries, getting our team back together... And look at these players. These players are winners."
Cardinale later spoke of the emotion he felt as he left the stadium.
"It makes me want to cry. It's fantastic. The best night. We will build on this."
The comments reflected the significance of the victory for the Milan hierarchy, with the club having faced criticism in the days leading up to the derby.
Head coach Ruben Amorim also acknowledged the pressure surrounding the club, saying he understood the criticism and was pleased for Cardinale.
"I'm really happy for Cardinale because I know the whole story. I know it has not been easy, it is not easy and it will not be easy," Amorim said.
"But I can guarantee that everyone inside the club and at Milanello wants this objective very much. We will do everything to bring the club back to where it deserves to be."
Amorim nevertheless warned against treating the derby result as a turning point that would automatically resolve AC Milan's problems.
He stressed that the victory represented three points, just as the team had lost three against Bologna, and that consistent performances would be needed to make meaningful progress.
For Cardinale, however, the occasion was one to savour. The Milan owner made clear his belief in the players and the ambition to build on a result that had lifted the atmosphere around the club.