Montolivo, who was one booking away from a suspension, was cautioned for dissent in a 2-2 draw with Roma.
Allegri conceded it was a flawed performance but while he admitted some luck had gone Milan's way he insisted the Rossoneri played as well as they could given the absence of two key defenders as well as Brazilian playmaker Kaka and midfielder Montolivo.
Juventus are now nine points ahead of Napoli with Milan a further two points adrift and Fiorentina, despite a 2-1 reverse away to Cagliari, sit fourth, one point ahead of Lazio.
With a contract until the 2014 World Cup in Brazil, coach Joachim Loew has said Germany has a bright future despite their Euro 2012 semi-final exit at the hands of Italy.
Massimiliano Allegri is set to extend his contract as coach of Italian champions AC Milan to 2014, the club's chief executive Adriano Galliani announced on Monday.