Mihajlovic has overseen an uninspiring campaign to date and was grateful for the support he received from owner Silvio Berlusconi ahead of the weekend's clash at San Siro.
Carlos Bacca netted a fourth-minute opener and Kevin-Prince Boateng came off the bench to score the first goal of his second spell at Milan and seal the points.
Former Serbia international Mihajlovic believes his side have provided a template for success over the coming months and stated his intention to return to a 4-3-1-2 formation due to the availability of Boateng and fit-again Mario Balotelli.
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"I am very happy, I have to thank the guys, we have ended a complicated week in the best way," he told a news conference.
"I hope this half of the season will be the round of revenge and vengeance. The goal is to try to play this way and climb up the rankings.
"When we have everyone available, my idea is to return to 4-3-1-2. Boateng and Balotelli have shown that when they are well they make the difference. Prince deserves this."
Mihajlovic's squad could be bolstered further in January according to Milan chief executive Adriano Galliani, who discussed a number of transfer targets.
Galliani said River Plate left-back Leonel Vangioni could arrive this month, while interest in Zenit St Petersburg midfielder Axel Witsel would most likely wait until the close season.
"Let's see if we can anticipate the arrival of Vangioni from River in January," he told Mediaset Premium. "Witsel I do not think it will move now, but he may do so in July."
Galliani added that a move for Inter defender Andrea Ranocchia was "more no than yes" and expressed an interest in Ajax winger Anwar El Ghazi – with the caveat that Alessio Cerci and Stephan El Shaarawy must be moved on before any move for the Dutch international would be considered.
El Shaarawy is reportedly a target for Roma after he fell out of favour in his season-long loan at Monaco, but Galliani claimed the Ligue 1 side would have activated an obligation to buy the attacker in the loan deal had he made 25 appearances.
The Italy international played 24 times before being frozen out, leading the Milan chief to criticise Monaco's behaviour.
"Monaco at game 25 had the obligation to buy El Shaarawy," Galliani added.
"They made him play 24 games and they don't want him to play anymore, they told us this.
"He was a minute away from being bought. The media can define their behaviour. Calling it 'bizarre' is putting it nicely."