Massimiliano Allegri's men were beaten 2-1 at the Stadio Marc'Antonio Bentegodi on Saturday, with a Luca Toni double securing the three points.
Montolivo believes Milan switched off after going ahead through Andrea Poli 14 minutes in.
"Clearly we stopped playing after the first goal, everyone has to take a look at themselves, we got exposed to their counter-attacks," said the former Fiorentina midfielder.
"Each of us must look at ourselves and give something more to win games, fortunately we have an important match and we will look to make up for everything."
Milan won just once in their opening four games last season and needed a dramatic win in the last match against Siena to finish in the final UEFA Champions League place.
Montolivo wants Milan to avoid repeating their start in the last campaign and has targeted a win in the Champions League play-off second leg against PSV on Wednesday.
"We cannot make a repeat of how we started last season, luckily we have this crucial match on Wednesday," he continued.
"We know it is a crossroads for our season, we have to turn the page and focus on this match at the San Siro."
Milan drew the first leg at the Philips Stadion 1-1 on Tuesday, with Tim Matavz's equaliser cancelling out Stephan El Shaarawy's opener.
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