The Rossoneri have not graced Europe's top table since the 2013-2014 season and are playing in continental competition for the first time since that campaign in the UEFA Europa League this term – Milan having won the first leg of a third-round qualifier against CSU Craiova this week.
Milan have been on a heavy recruitment drive during the transfer window, funded by their new wealthy Chinese owners, with the likes of Leonardo Bonucci, Andre Silva, Lucas Biglia and Ricardo Rodriguez having moving to San Siro.
The big spending has only increased expectations among supporters and the club's hierarchy, but head coach Montella is not fazed by the pressure.
"The agreement with the club is that we must not waste the enthusiasm of the fans, let alone disappoint expectations," he told Corriere dello Sport.
"We must become a team as quickly as possible and try to achieve our objective of Champions League qualification.
"If we were to miss out on that target, it would certainly be a very damaging blow both economically and in terms of image.
"However, there is a great deal of competition in Italy and there are teams who, even if they haven't had our summer transfer strategy, are still slightly ahead of us in terms of planning.
"We have chosen players who are ready to go and can give a great deal, who are top players for our level and for Italian football.
"I therefore think that the potential is there and it's only a matter of time.
"We have some certainties and some players who can grow over time."
He added: "Anyone who does this profession cannot duck responsibility. So yes, I am happy with the team that has been put together.
"I feel a lot of responsibility, but I am also very, very motivated."
The signing of Bonucci from Serie A rivals Juventus was a particularly unexpected coup for Milan.
The Italy centre-back has been touted as a potential captain this season, but, while accepting that is a possibility, Montella is keeping his options open for now.
"Bonucci is a candidate alongside Lucas Biglia," he said.
"I am taking time over it, because I think the choice must be shared with the club, the coach and the squad.
"The fans must also feel they are represented in this decision."