Dan Ndoye struck the only goal of the night as Bologna won a trophy for the first time in 51 years.
"After some disappointments, I think we deserved this, especially as we played a great game tonight. It was an incredible performance, we knew once again what Milan would do in the second half, so we responded,” Italiano told Sport Mediaset.
“This incredible year is crowned with this trophy, which is what these fans deserved."
The win ends a run of three consecutive defeats in finals with Fiorentina for Italiano, who in two years lost the Europa Conference League final twice and also the Coppa Italia final.
"Those too were three very big disappointments. I didn’t honestly think I could get straight back out there and win it, but I did. I dedicate it to these lads, who are extraordinary,” he said, before paying tribute to former Fiorentina director Joe Barone, who passed away last season.
“I also want to send a dedication to Joe Barone’s family, because his son sent me a message this morning and I was immensely pleased. We came so close to lifting silverware with him too and they mean a lot to me.”