Head coach Massimiliano Allegri blamed bad luck for Milan's defeat in his post-match press conference, but Montolivo feels there's more to the loss than just misfortune, and believes they're by no means on top of their game yet.
"There’s still a lot of work to do in all areas and we still have to find the right balance. There’s a lot of room for improvement," Montolivo was quoted as saying on the club's official website.
"I would have expected a different result for the first game of the season. I can understand the discontent of the fans and we’re disappointed and angry too, but we’re counting on making amends on Saturday.
"It was tough to get the ball in and around the final third, but when teams close up like they did here today it’s difficult to create play. We’re disappointed because we created a lot in the second half but we were missing that little bit of luck."
Milan resume Serie A action away against Bologna on Saturday.