A double from Amauri helped Parma to a 2-0 win over relegated Livorno which ended Milan's hopes of sealing a sixth place finish in Italy's Serie A and a place in next season's Europa League.
Parma's 15th win of the campaign mean they finish one point ahead of Torino, in seventh, with Milan in eighth also on 57 points despite a 2-1 win at home to Sassuolo.
Torino, Parma, AC Milan and Verona had been battling for sixth spot and a place in the Europa League.
Sixth place was good enough to qualify for Europe because Italian Cup winners Napoli had qualified for the Champions League and Fiorentina, the beaten finalists, were already guaranteed a Europa League place themselves.
Torino and Verona arguably had the toughest tasks away to Fiorentina and Napoli respectively.
Torino, however, took the game to Fiorentina and only narrowly missed out on the win that would have secured their return to European competition when Alessio Cerci missed a spot-kick in injury time.
Verona suffered a 5-1 rout at Napoli, for whom Duvan Zapata and Dries Mertens scored a brace.