"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'".
Central defender Medhi Benatia struck twice for Juventus and Douglas Costa was also on target on an unhappy evening for Milan goalkeeper Gianluigi Donnarumma who was at fault for the second and third goals.
Juventus crushed AC Milan 4-0 on Wednesday to win a fourth consecutive Italian Cup.
"At this moment Donnarumma is the Milan goalkeeper, the rest is down to the club", Gattuso told Rai Sport.
A graduate of Milan's youth academy, Donnarumma's first game for the senior team came in a 2-1 win over Sassuolo on October 16, 2015.
"I am the coach, all I do is train the players who are put at my disposal".
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But as Buffon kept his net clean Donnarumma finished the night in tears after a game to forget.
Morocco global Mehdi Benatia broke the deadlock for the hosts 10 minutes into the second stanza with a free header inside the box, 1-0.
Gattuso's men still had some fight left in them at least for pride's sake with five minutes remaining, but they were unable to carve out a chance as Juve ran out big winners on the night.
An own goal by substitute Nikola Kalinic completed a calamitous defensive display by Milan.
"Juve always do something special, it's not the first time. I felt bad for a few days, but fortunately the lads completed the job and I thank them for being close to me".
Milan are sixth in Serie A and have not won a major trophy since now Juventus coach Massimiliano Allegri led them to the Serie A title in 2011.