Ten-man Bologna came from behind to stun the Nerazzurri thanks to late goals from Musa Juwara and Musa Barrow.
Inter Milan slipped further behind in the Serie A title race with their fourth defeat of the season.
In an interview with the media after the game, Conte expressed his disappointment in his team’s display against Sinisa Mihajlovic’s men, and insists the players must also be overwhelmed with guilt.
“We all have to take our share of the responsibility. First of all, me as the coach, then the players who step on to that pitch,” the former Juventus and Chelsea boss told Football Italia.
“I think we gifted Bologna the game today and it’s not the first time. It happens often, both during the regular season and since the restart.
“There are certainly some situations and evaluations we need to look at.”
“It’s not the first time and we have to ask ourselves questions now, both myself and the players.”
Conte and Inter Milan will now face Hellas Verona at Stadio Marc'Antonio Bentegodi on Thursday night.