Morata arrived last month from Atletico Madrid.
Gabbia told DAZN: “Alvaro is definitely a champion, he brought not only technical qualities but also a lot of leadership and personality.
"Obviously we miss him, without taking anything away from those who are playing at the moment.
“He is a player who, even if he doesn’t play and only trains, transmits a lot, he is a really important part of the group. The team and I are happy that he is here, he will give us a big hand.”
He also said: “The role that Milan must have in the championship and in the Champions League is a leading role. We must try to play all the games in the best possible way, leaving everything we have on the pitch.
“Then at the end of the year we will see what work we have done but the Milan shirt requires you to always aim for the maximum and that is what we will do.”