Bologna suffered a 2-0 defeat against Genoa on Friday in Thiago Motta's final match in charge as their remarkable Serie A season concluded disappointingly.
Despite securing a top-five finish and a spot in the next season's Champions League, Bologna can no longer overtake Juventus for the third position.
Ruslan Malinovskyi scored early to give mid-table Genoa the lead, with Vitinha sealing the victory just before the hour mark.
Former Italy midfielder Motta will not extend his contract with Bologna, which ends in June, after two years at the helm, as announced on Thursday.
Motta is reportedly set to take over from the dismissed Massimiliano Allegri at Juventus.
"I am focused on the present and not concerned about the future at the moment," said the ex-Paris Saint-Germain and Barcelona player to DAZN.
"The two seasons spent here were fantastic and will remain as one of the highlights of my career. We have completed a two-year cycle.
"I will miss my players. I may no longer be their coach starting tonight, but I will always be a friend, a big brother, and even a father figure to some, and they know they can reach out to me anytime."
Bologna's sole previous participation in Europe's elite club competition was a preliminary round defeat to Anderlecht in the 1964-65 European Cup.