Bologna slipped to a 2-0 loss at Genoa on Friday in Thiago Motta's last game in charge as their historic Serie A campaign came to an underwhelming end.
The visitors had already wrapped up a top-five finish and a place in next season's Champions League, but can no longer come third ahead of Juventus.
Ruslan Malinovskyi put mid-table Genoa ahead early on, before Vitinha clinched victory just before the hour mark.
Former Italy midfielder Motta will not renew his contract with Bologna, which expires at the end of June, following two years in charge, it was announced on Thursday.
Motta is widely reported to be replacing the sacked Massimiliano Allegri at Juventus.
"The future doesn't matter much at the moment, I want to focus on the present," the former Paris Saint-Germain and Barcelona player told DAZN.
"The two seasons spent here were wonderful and will be one of the greatest memories of my career. We completed a two-year cycle.
"I will miss my players. I'm no longer their coach as of tonight, but a friend, a big brother, even a dad for some and they know that they can always contact me about anything."
Bologna's only previous appearance in Europe's top club competition was a preliminary round loss to Anderlecht in the 1964-65 European Cup.