Riccardo Orsolini had Bologna ahead, before the Rossoneri stormed back through Santiago Gimenez (2) and Christian Pulisic.
Conceicao told Sky Italia afterwards: “It wasn’t a great performance. It’s true, we won against a team that has been doing very well in Serie A, the Coppa Italia and the Champions League.
"They are tough because they press you man for man, so if we don’t do well to find the spaces, we get that poor first half.
“We conceded the first goal because we tried to press a bit higher and were caught out.
"I changed the system to a 4-4-2, the players gave a strong response and those who came off the bench also gave a positive response. This is the kind of spirit I like about this side.”
Conceicao not important here
Meanwhile, Conceicao was pushed about his own future, with doubts persisting over his position despite Milan's revival.
He, however, would only say: “Conceicao is not important here. What is important is the next game and winning a trophy. An historic club like Milan cannot be content to sit ninth in Serie A. There are regrets and frustration from everyone at the way this season went.
“I am accustomed to certain things. This is not the moment to talk about me. At the right moment, I will speak.”