The former Primavera youth team boss was promoted to the senior bench in April to replace sacked Sinisa Mihajlovic.
“I have a very particular personality and am a very humble person," said Brocchi at his Brescia Press conference.
“As a player I achieved great things by starting from the bottom. I found myself in an important family like Milan, a wonderful adventure in the youth academy and had the good fortune to become Coach of the senior squad.
“It is fundamental for me to feel supported, so people have confidence in me. We did not have the right conditions to continue, so my decision to walk away was right for the good of the club and the good of Berlusconi.
“I would not have worked with the right sense of calm. I wanted to show what I can do without prejudice. I am very happy to have become the Coach of Brescia, a club that is very important in my life.
“I want to bring my ideas to the locker room with the hope of finding the right synchronicity and achieving success."