Balotelli made his debut for Liverpool in their 3-0 win over Tottenham on Sunday after having left San Siro in a €20 million (£15.8m) deal earlier in August.
Milan made light of the striker's absence in their opening Serie A game, beating Lazio 3-1 in convincing style, and Abate does not believe that the former Manchester City forward's loss will be keenly felt in the coming campaign.
"The coach [Pippo Inzaghi] said a very important thing in his press conference, which is that the man comes before the player," he told Sky Sport Italia.
"Mario is a truly great player but he needs to improve in other areas. He needs to take on a lot more responsibility.
"I think that, in this group, we have got a good mix of experience and youth, but must not get ahead of ourselves."
Goals from Jeremy Menez, Sulley Muntari and Keisuke Honda sealed the win for Inzaghi in his first Serie A match in charge of Milan and Abate feels that the squad have recaptured some of their identity under their former striker.
"Inzaghi is like one of the group," he added. "This season, I think we can achieve great things together. He really fired us up and I think the Milan DNA has returned."