Dortmund were beaten finalists in the competition last season, but the loss on Tuesday was the club's fourth in a row in all competitions. In the Bundesliga, Dortmund sit 10th, 20 points behind leaders Bayern Munich.
Sahin was assistant to former Dortmund coach Edin Terzic in last season's surprise run to the Champions League final where they lost to Real Madrid and was promoted to head coach in the summer.
"We have unfortunately lost faith that we will achieve our sporting goals," sporting CEO Lars Ricken said of the current management. Ricken said the decision "hurts... but was unavoidable after the game in Bologna.
German media reported potential successors included former Manchester United boss Erik Ten Hag, who has been seen watching Dortmund games recently, or one-time Benfica and Bayer Leverkusen manager Roger Schmidt.