"It's incredible. At one point in the season, we said, 'if we want to be monsters, we have to win the Scudetto again try to win the Coppa Italia and the Champions League'".
The young goalkeeper had a hard night in Wednesday's Coppa Italia Cup final making two howlers as Juventus won the match 4-0 to lift the trophy for the fourth consecutive year.
The Rossoneri were beaten 4-0 last night, with goalkeeper Gianluigi Donnarumma making two glaring errors which led to goals.
Milan lost the Italian Cup final to Juventus in 2016, but beat the Turin side for the Italian Super Cup in Doha later that year.
"It's not that Juve have to win, but I'm now unfortunately used to the idea that people take our victories for granted", said Allegri, 50, after achieving his tenth coach as a coach between Juventus and former club AC Milan.
Donnarumma has not missed a Serie A match this season, appearing in all 36 games, conceding 40 goals.
But as Buffon kept his net clean Donnarumma finished the night in tears after a game to forget.
The first half was quiet - Buffon and Donnarumma on two made five saves, serious threats at the gate of both commands was not observed.
Gattuso ran onto the pitch to calm down his players.
Bosnia internional Pjanic told the club website: "We really wanted to win every trophy available this year".
"I know that I am being judged for what I am doing each day, the duration of my contract is not important, but we need to understand who we are now, we need to think about the next 180 minutes, because the repercussions of this defeat may be hard".