The host side needed an injury-time equaliser from Nicolo Barella just to earn on a point, with Peter Olayinka having given the Czech side a deserved lead.
With Group F also containing Barcelona and Borussia Dortmund, the result represents a missed opportunity for Inter and Conte could offer no excuses.
"Slavia Prague certainly played in a very European way, aggressive and with intensity," the Inter manager said. "We didn't do well to find solutions and get around that. In other games, we were up against sides who sat back and waited for us, whereas Slavia attacked us. We struggled and to be honest I am not satisfied with the performance.
"I must be the first to take responsibility, because evidently I didn't have the effect I wanted in my initial choices or in explaining the kind of match we were going into.
"We could've done far better, this is not the kind of football we are training to play. We've got to improve in terms of character too, but when I talk about a growth process, it goes through games like this too, as I know what kind of situation this is."
The nature of the performance was a concern to Conte, who suggested his side had plenty of room for growth, but warned fans not to expect instant results.
"Slavia beat us in terms of intensity, determination, pace," said the former Chelsea boss. "We showed nothing of our ideas of football. You seem to think I arrive here, touch and the ducklings turn into swans.
"There's a lot of work to do and we need to improve, but that was not our football. When I say we shouldn't let ourselves get swept up in enthusiasm, I mean it. I am here to help these lads improve, so put the blame on me.
"I refuse to talk about individuals, because we were all below par, starting from me. I am the first onto the naughty step, the main dunce.
"I generally hate the long ball and run routine, as that is not our football, but that's what we largely did. It wasn't the plan."