Mauro Icardi completed his hat-trick from the penalty spot in the final minute, having already twice given Luciano Spalletti’s high-flyers the lead.
A brilliant effort from distance by Suso and a Samir Handanovic own goal had Milan within touching distance of a point after a thrilling second-half rally, but Montella was left angered by the decision to penalise Ricardo Rodriguez for impeding Danilo D’Ambrosio in the area.
Despite lavish close-season investment, Milan have now lost four and won four of eight Serie A matches so far this season, and reports this week linked Switzerland’s former Lazio boss Vladimir Petkovic with Montella’s post.
Nevertheless, Fassone was unequivocal in his backing for the 43-year-old when he spoke to Milan TV after Sunday’s match.
“We certainly go along with Vincenzo,” he said. “When we are reconstructing our [club] we need to give time and tools.
“Now we see the first positive signs. Montella will absolutely have the time to continue working.”
Fassone added: “Derbies are always an amazing thing. This time it turned badly for us and they celebrated with their fans.
“The next time, I am convinced it will be nice for our fans. The second half seemed like a completely different game and, with quality and attitude, we closed Inter in their half of the field.
“[Tenth in the table] is not a position for Milan and we have to roll our sleeves up, but we have received good indications.”
Milan host AEK Athens in the Europa League on Thursday and will aim to break a run of three consecutive Serie A defeats when Genoa visit San Siro next weekend.
