While the 19-year-old Donnarumma could not be blamed for Medhi Benatia's opener in the final, his mistakes led to the ensuing goals from Douglas Costa and Benatia.
Bonaventura also defended goalkeeper Gigio Donnarumma after two blunders on the night. Then Kalinic headed a corner into his own net.
Juve, who have won a Serie A and Coppa Italia double for three seasons in a row under coach Massimiliano Allegri and the Italian boss will be eyeing the same for the fourth consecutive time with the league title all but sealed.
Juventus has won a total of 13 Italian Cups, at least four more than any other team.
"This is like the World Cup final for our enthusiasm, the enthusiasm of the fans and their desire to get back to lifting a trophy again", 2006 World Cup victor Gattuso told a press conference on Tuesday on the eve of the game at Rome's Stadio Olimpico.
Milan's coach Gennaro Gattuso, meanwhile, stuck with his usual attacking trio of Hakan Calhanoglu, Suso Fernandez Saez and Patrick Cutrone, who leads the team in scoring with 16 goals.
Unfortunately, that proved to be the trend for the rest of the first half as the sides went into the break goalless. In the second leg, Pjanic scored a penalty 15 minutes from time when Blaise Matuidi was fouled in the area to hand Juve a 2-0 win on aggregate.
It got worse for Milan with 15 minutes remaining as striker Nikola Kalinić headed Mirlam Pjanic's cross into his own net to make it 4-0 to Juve. We'll do this with Juventus administration.
"The lads had an extraordinary game and deserved this win".
"We didn't succeed in the Champions League, but we still did something unimaginable".
"Today I feel this incredible pressure on me, as if the fans were on my shoulders", said the 40-year-old.
"I'm also sorry if anyone who isn't a sportsman and has never tried to stay in a group doesn't know how many sacrifices, how much energy, how much tenacity and how much damnation it takes to win like we have".