Question marks over Massimiliano Allegri's future as AC Milan coach have begun to appear in the media a day after the Rossoneri's second home defeat of the season.

Milan, who begin their Champions League group campaign against Belgian side Anderlecht on Tuesday, suffered a shock 1-0 home defeat to Atalanta on Saturday.

It came three weeks after defeat to Sampdoria at the San Siro and a fortnight after Allegri's side appeared to be on the mend with a 3-1 away win at Bologna courtesy of a Giampaolo Pazzini hat-trick.

Allegri's relationship with club vice-president Adriano Galliani is said to be deteriorating and reports last week claimed club owner Silvio Berlusconi was beginning to take "more interest" in the club's situation.

Corriere dello Sport said on Sunday it was Milan's worst start at home in 82 years, and the defeat would create an even more "delicate" situation between Allegri and Galliani.

Milan lost the spine of their team earlier this summer after selling Zlatan Ibrahimovic and Thiago Silva to Paris Saint Germain, as well as seeing several established veterans such as Filippo Inzaghi retire.

Team captain Massimo Ambrosini, who was substituted in the second half and was later seen talking with an increasingly frustrated Allegri, said their departure should be no excuse.

"We need time to accept that this team has changed... but the fact they have left should not be an excuse," said Ambrosini, one of several Milan players guilty of not converting chances having dominated for long periods.

In the end, Atalanta soaked up the pressure and stunned the San Siro when Luca Cigarini struck a 65th-minute winner past Christian Abbiati.

Allegri believes his side's problem is "mental" and called on his players to have more conviction in their abilities.

"We must have faith in ourselves and play fearlessly," he said.

"The guys have to grow up and realise that playing with fear doesn't get us anywhere."