Serie A giants Milan have endured a testing campaign, and sit 42 points adrift of leaders Juventus in 10th position.
Clarence Seedorf's side have an opportunity to secure a rare high point in a season of lows, when they face rivals Inter at San Siro this weekend.
Captain Montolivo feels that the slim opportunity to reach the UEFA Europa League and to avenge December's 1-0 defeat in the reverse fixture has provided extra motivation, but added that three points will not be enough to excuse a disappointing season.
Speaking to Corriere dello Sport, he said: "First of all, for us this should be a derby of pride, to redeem a season that has not been great and to try to take a Europa League qualification place, and to avenge the derby from the first round.
"In short, for many reasons, we want to win. However, it is not that one game, even if it is the derby, can lift an entire season from being negative.
"I would like to win more now that I have the captain's armband. With Inter we are six points behind and with only three rounds to play.
"But we cannot make calculations. If we go and win then it goes to within three and it changes the discourse."
