Tammy Abraham had Milan ahead before Hakan Calhanoglu struck an equaliser from distance.
Afterwards, a pleased Conceicao declared: “I think the result was fair, now we wait for the second leg and have this chance to go to the Final in Rome, which we all really want.
“I would like to thank the crowd, who were fantastic this evening in their support for the team. The players understood what they were supposed to do, it was a balanced match against a difficult opponent where we had to be intelligent defensively, we did that, and I am happy with it.
“We too had chances, I didn’t see Inter make that many moves to go clear. They had two set plays in the first half that caused problems, we knew they were strong on those situations, but it was overall pretty even and the result was fair.
“I am truly happy with this approach and attitude. The second half against Napoli was also good, so we must continue this evolution to reach our objective, which is to reach the Coppa Italia Final and win the trophy.”
Conceicao also insists he can see an improvement and progress in the team after Wednesday night's result.
“When I arrived, we had two games against Juventus and Inter for the Supercoppa, then we started a series of matches playing every three days. Over the last two weeks, I’ve had more time to work with the squad in training on situations that are fundamental to bring more balance and reassurance,” he added.
“I know that might seem like an excuse, but it’s the truth to me, because you get intensity and aggression in training too. Now we are working on the pitch and not just in video lectures, which makes a difference.
“In the second half against Napoli and again tonight, I saw a more solid team, the kind that I like to see,”