The Italy international felt a share of the spoils was a decent outcome for the Rossoneri given that they had had Mathieu Flamini sent off with 17 minutes to go
Mathieu Flamini, who had opened the scoring only to see his goal cancelled out almost immediately by Goran Pandev, was dismissed 17 minutes from time for a reckless two-footed challenge on Juan Camilo Zuniga.
However, Milan survived a tense finale to secure a precious point which keeps their hopes of pipping Napoli to second place alive.
"This evening we have truly expended a lot of energy," Montolivo told Mediaset Premium. "After being reduced to 10 men it was so important not to lose and to remain in the race [for the Champions League].
"Now we are still four behind Napoli but only four in front of Fiorentina [in fourth], so we must keep going right until the end of the season.
"We will face Juventus next Sunday and we will certainly have to give our all in Turin too."
Milan lacked a real cutting edge up front in the absence of Mario Balotelli, who was hit with a mandatory one-match ban for picking up his fifth booking of the season against Fiorentina last weekend before then being suspended for a further two games for insulting the officials at the Artemio Franchi.
However, Montolivo is praying that the Rossoneri launch a successful appeal and get Balotelli back on the field in time for their trip to Turin.
"He is important to us," the former Viola captain admitted. "We still hope to see him again against Juve, but those who replace him can also do very well."