The Curva Sud (South Curve) fan group issued a statement praising Allegri for his handling of a young squad last season, when Milan recovered from a poor start to finish third in Serie A and qualify for next season's Champions League play-off.
"Today, we find ourselves with a project which has only just started and which will soon be dismantled by presidential choice," said the statement on the group's website.
The fans were especially critical of reports that former Milan midfielder Clarence Seedorf, who has no coaching experience and is playing with Botafogo in Brazil, could be brought in as a replacement.
"We can well understand, but not agree, that whoever invests can decide to change coach just for personal reasons," they said.
"But if it's really part of a plan we must at least start again by putting the team into the hands of an experienced trainer," the fan group added.
"Certainly not someone like Seedorf or others who have zero experience on the bench and will come in to take in hand a squad of young players one month before the first official engagement and before the very difficult task which is the preliminaries of the Champions League.
"We hope that there will be respect for Milan as an institution and its fans, with a choice which is not just related to a particular moment, but with the continuation of a project which we decided to support to the end one year ago."
The fans said they recognised that Allegri was having to rebuild the team after club management slashed the wage bill and held a firesale of top players the previous summer in a bid to cut costs.
"The championship started with great difficulty and Allegri's Milan appeared destined for the abyss. Aware that criticism would be detrimental to the atmosphere in the team, we decided to support Milan at the most difficult moment.
"Our choice paid off. We created a sort of tacit agreement between the ultras, the coach and the team, that we would all row in the same direction... we began to reap the rewards with the performances of [Stephan] El Shaaraway and careful management of players from coach Allegri, who we recognise has been carrying this project."
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