Montella's new-look Milan crashed to another loss on Sunday, this time beaten by Scudetto contenders and visitors Roma 2-0 at San Siro.
Milan finished the match with 10 men after off-season recruit Hakan Calhanoglu received a second yellow card in the 80th minute as pressure mounts on Montella, who has already overseen three defeats in seven league matches this term.
Ancelotti – who guided Milan to Serie A, Champions League, Coppa Italia, Supercoppa Italiana, UEFA Super Cup and Club World Cup titles during his tenure – was sacked by Bayern Munich on Thursday and immediately linked with the Rossoneri but Mirabelli backed Montella post-match.
"We are only seven rounds in, we have a new team, so no coach has a magic wand," Mirabelli told Sky Sport Italia.
"You can't get certain results straight away. We have a group of players who need to become a team, so as far as we are concerned, Montella is working well. We just have to hope that work brings important results.
"We must try not to look at the table. Roma have a well-drilled unit who have been playing together for years. It's not easy to face them and do as well as Milan did. We see positives in this defeat too."
Milan are seventh in the Serie A standings, nine points adrift of leaders Napoli heading into the international break.