Bologna crushed Conte’s men at the San Siro Stadium, on account of two second half late goals from Musa Juwara and Musa Barrow.
Romelu Lukaku scored in the first half for Inter.
Responding, Conte, who was frustrated with the outcome, said he was liable for the result of the experience.
“There’s a great, indeed enormous, disappointment,” Conte said at the post-match press conference after the game.
“We managed to lose a match that we should have brought home comfortably. I’m angry with myself as the coach and responsible for what happens on the pitch.
“The players must also be angry with themselves, although they only have a small part of the blame.”
Inter Milan’s next Serie A match is against Verona on Thursday.