Gabbia settled the game for Milan 2-1 in their favour on Sunday.
He said afterwards: "I felt those six derbies very much on me also because of my history, but I have to tell you the truth, everyone in the team, even Tammy who recently arrived, Fofana, but everyone, really, understood the importance of this match, the weight it had for us.
"Consequently we are happy this evening and it is right that we enjoy it this evening, that we celebrate a beautiful victory then from tomorrow we will start preparing for the next match because in any case this one, even if beautiful, is always worth three points."
On the squad's spirit, Gabbia continued: "The attackers, all of them. Today even Chukwu who came in a little, but everyone really gave us an incredible hand. The group really pushed on the accelerator this evening. It must be a good starting point for us, we took a great satisfaction, but the spirit we really have to try to make sure is always this. Because we deserve it, so, in 11 who run and help each other all together, we can take some great satisfaction."
On his first ever derby goal, Gabbia also stated: "It was perfect because there wasn't even that much left (laughs), so there was less time, let's say, to suffer in the last minutes. I'm very happy. Obviously it's a dream come true, and nothing, it must be a great satisfaction for me too, but from tomorrow onwards we'll connect our minds to what the future is, which is the most important thing."