Mihajlovic had succeeded two AC Milan players-turned-managers in Clarence Seedorf and Filippo Inzaghi.
Milan are sixth in the table on 49 points with six games left, 15 points behind third placed Roma and no chance of a Champions League spot.
They might end up with some silverware if they win the Coppa Italia's final against Juventus on May 21 but Brocchi would not look so far ahead.
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"We cannot think about Juve, we have to win the matches ahead of us first of all," he said.
"I have adopted some of the characteristics (of coaches Cesare Prandelli and Carlo Ancelotti) and this will help me," he explained.
"Pinning our opponents back in their own half and pressing will be something that I will request. We must have an aggressive mentality."
Milan have a lacklustre squad and a possible sale of the club has been stalling lately, giving little hope of big changes in a club that have not won the Serie A title since 2011.
Brocchi, who was the club's youth team coach before he replaced Mihajlovic, will be keen to rely on some young players from the academy.
"We don’t have many matches left this season, but if there is a chance and opportunity, we have lots of interesting players from the youth sector."
"I have always wanted my teams to take the initiative and not sit back. But achieving that goal will take time," he said.
Leaders Juventus, who lead Napoli by six points, take on relegation-threatened Palermo on Sunday.
They welcome back in the squad Argentine striker Paulo Dybala, who took part in Wednesday's training session after sustaining a thigh injury.
Napoli travel to Inter Milan, who are fourth and trail Roma by six points.
(Writing by Julien Pretot; Editing by Amlan Chakraborty)
