Martin Cacares bagged a brace for the Bianconeri in his first appearance for the Italian outfit since his last loan spell at the club in 2010 to overcome Milan in the first leg of their semi-final showdown at the San Siro.
However, Allegri has told his team to remain calm.
"There is no pressure on us, because I know the strength of the team," he told RAI Sport. "We must continue to work to get out of this situation.
"Qualification is harder now, but nothing is compromised. We have lost a few too many times recently, but we must remain calm and confident about our own strength."
Meanwhile, Milan remain one point behind the Italian league leaders in Serie A.