The 53-year-old was announced as the new Rossoneri boss on a two-year deal on Thursday (AEST), the day after Marco Giampaolo's sacking was confirmed.
Some fans have already made their displeasure at the news known, with "#PioliOut" trending on social media given the coach's links with city rival Inter.
Pioli, Inter boss in 2016-2017 and said to have been a Nerazzurri fan as a child, says supporters are entitled to their view - but he is eager to prove them wrong.
"I have respect for the fans and they have the right to criticise, but this is an extra stimulus for me," he told reporters.
"I don't have social media and I'm not on there. If you find some profiles, they're not mine. I prefer people to criticise you while looking you in the eyes.
"The past is the past. I'm a man and a professional, who wants to do well. The judgements will be from what happens on the pitch, not from what I was as a child."
Pioli takes over a Milan side who have lost four of their opening seven Serie A matches of the season and are already four points adrift of the top four.
However, his goal is to instil some bravery into his players in order to get them back into the fight for a Champions League place.
"We'll be working on the players' heads as well as the set-up on the pitch. We've got 10 important days [in the international break] and I'll try to make the most of every moment," he said.
"[Giampaolo] is a good coach but he has different ideas. We start from a good level: I know this is a professional group, with top guys not only from a technical point of view but also a moral one.
"I'd like to make the team play in a positive way. I just have to give them all the courage possible.
"We have to fight to get into the Champions League."
Pioli's first game in charge will be at home to Lecce on October 20.