The 36-year-old veteran Rossoneri goalkeeper believes his side need to add more silverware this season, having not won anything in two years
The 36-year-old would love nothing more than to deliver them the Serie A title this season and he is also eager to enjoy victories in their derby games with Inter this campaign.
"We need to win a trophy, both for us and our fans," Abbiati told Corriere dello Sport.
"To win the Scudetto this season we need more consistency in our results. Antonio Conte's Juventus are the benchmark, seeing as they went an entire season unbeaten.
"The [Milan] derby has a different feeling to any other game. It's a great game that hurts so much to lose. Inter won't be happy after finishing behind us in Serie A last season, but we will be focused on winning both games for our supporters."
Abbiati also claims that, while Riccardo Montolivo is an excellent choice as captain, he would be proud to lead the side if he is called upon.
"The captain's armband is in good hands with Montolivo," he continued. "Of course I would love to wear it, who wouldn't? It would be a great honour."
The Italian, who has four caps for the Azzurri, added that Champions League qualification is the bare minimum this season and believes Mario Balotelli will be key to any success they achieve.
"We have to qualify for the Champions League again this season, at worst, and I believe Balotelli will help inspire us to a top three finish," he concluded.
Milan secured third place - and, as a result, a place in the Champions League play-off round - on the final matchday of the last Serie A season.