The Italy international was satisfied with his side's display, but was quite disappointed with the outcome of the game as he feels the Rossoneri deserved more
Walter Samuel gifted Andrea Stramaccioni's side an early lead in the Derby della Madonnina and the hosts were unable to get back in the game in the remainder of the match as they failed to find the net at San Siro.
"I think it’s been our best game of the season, we deserved to win. There was only one team on the pitch, especially after [Yuto] Nagatomo got sent off," Montolivo was quoted as saying on the club's official website.
"It’s tough because we deserved it. We played really well. Inter played defensively, they were good but lucky as well.
"Now we have the international break and then we’ll get back to work against Lazio and we have to start getting points.
"If we had six or seven points extra we could take a hit like this, but we have so few now and we didn’t need this defeat."
The midfielder then went on to stress that his goal was wrongly disallowed, while he also felt Milan should have been awarded a spot kick.
"It’s a shame about the disallowed goal. On the pitch, the impression I had was that it should have stood. It’s disappointing because it was a great goal, from far out and a tough shot to make.
"Even the penalty shout with Robinho was a cert. Regardless of how strong the contact was, the intention was clear and it should have been punished."
Milan have dropped to 11th spot in the table with seven points from as many games.