The outfit dismissed coach Massimiliano Allegri on Monday, less than 24 hours after a 4-3 defeat at Sassuolo - a result that left the team 30 points behind Serie A leaders Juventus at the halfway stage of the campaign.
A statement from the fans (Curva Sud) read: "The Curva Sud wishes to thank Mr Allegri, who after a logical decision from the club, parts company with Milan.
"We wish to thank him for the Scudetto and for the qualification to the Champions League, but above all for the man he has proved to be!"
Allegri led Milan to a Scudetto and an Italian Super Cup in his first season in charge (2010-11) but endured a frustrating campaign in Serie A.
Milan have won five and lost seven of their 19 league games and are currently 11th in the table and just six points clear of the drop zone.
The Rossoneri parted company with sporting director Ariedo Braida earlier this month to end his 27-year working relationship with Milan.
Back in December, the club underwent a board restructuring with club owner Silvio Berlusconi's daughter, Barbara, appointed as vice-president of the club.
Long-time vice-president and club administrator Adriano Galliani kept his job despite rumours he might be shown the door and he has since had to share responsibility for the day-to-day running of the club with Barbara, and the tension has not gone unnoticed.
The ultras' statement continued: "Now we wait with confidence to see what happens next, without forgetting that the total absence of a project for the future and a transfer market that has had little significance are the main causes of Milan's ailments!
"Let us not forget the uncomfortable seat that is shared by two (Adriano Galliani and Barbara Berlusconi) and the leadership that dampens the story of this club that is our life."
Assistant Milan coach Mauro Tassotti has taken temporary charge of the team and will guide the Rossoneri in Wednesday's last 16 Coppa Italia match against Spezia.
Former AC Milan star Clarence Seedorf is a leading candidate to replace Allegri.
The 37-year-old Seedorf is playing at Brazilian side Botafogo, a club he joined in 2012 after a 10-year career at Milan.
Seedorf has a coaching badge but has no managerial experience.
Former AC Milan coach and current Real Madrid manager Carlo Ancelotti does not believe this would hinder the Rossoneri, though.
"It's not the first time that Milan would make a choice like this one," he said. "It happened with Arrigo Sacchi and with Fabio Capello and in both occasions, things went very well.
"I know Clarence very well as he was one of my players and has always shown great personality.
"I believe that he has the knowledge and the capacity to do anything he wants in football.
"He would face a new experience in a club he knows very well and this is important.
"I wish Milan and Seedorf the best of luck."