Mihajlovic selected a Rossoneri side that put Inter to the sword at San Siro. Alex powered home an early header before Carlos Bacca and M'Baye Niang confirmed the outcome in the second half.
"For me it's been the greatest joy I've experienced since becoming a coach," Mihajlovic told Sky Italia cameras after the 3-0 win. "It's always the winners who go down in history.
"I'm happy for the president (Silvio Berlusconi), too, because he's our biggest fan. Hopefully we'll manage to get revenge on a few teams during this second half of the season."
Milan started the current campaign poorly and the three points from the Derby della Madonnina were only good enough to strengthen their hold on sixth place.
Their boss therefore spent much of the autumn fielding questions about his future in the dugout and feels this result will convince his detractors he is the right man for the job.
Mihajlovic added: "I have always been clear on this point. My conscience is clear because I know I have always given my all."
Referring to his opposite number, Roberto Mancini, who was sent to the stands for protesting when Inter were not awarded a penalty, Mihajlovic claimed his rival's apparent strength was a weakness.
"Roberto has so many options in his squad, and for me it's harder to pick a team when you have so much choice," he added.
"I believe that when things are going well you have to make as few changes as possible. When I decide we're going to play in a certain way I stand by my choices and will not chop and change."
Mancini, meanwhile, apologised to the Inter fans who witnessed their heaviest derby defeat in almost five years.
Inter have slipped to fourth having led the Serie A table until shortly after Christmas.
"Obviously recent results have not been good," he told inter.it. "We've played really well in some games, but this has not been a good time for us.
"Unfortunately we lost tonight and I must congratulate Milan, even though I don't think the nature of the result reflected what we all saw out there.
"It's been difficult but all we can do is say sorry and roll up our sleeves. It'll all come together."
Inter might have equalised midway through the second half but substitute Mauro Icardi - the captain started on the bench - missed a penalty against 16-year-old goalkeeper Gianluigi Donnarumma.
