The loss confirmed Milan will not be playing in Europe next season.
Conceicao admits the Coppa Italia final defeat last week to Bologna was a heavy blow for the players.
“The mood was not easy to deal with after the Final, with incidents not just then, but throughout my five months here that did not go our way. They are always negative for us and positive for the opposition, either through our own errors or those of others,” said Conceicao, who was upset seeing Santiago Gimenez sent off.
“We are challenging for Europe here. I admit we should’ve done much more in the Final, but these details become difficult to sustain. It was already a tough game away to Roma, let alone after going down to 10 men.
“We tried to give our all, Roma barely touched the ball for long periods in the first half and I felt we could’ve won. We cannot concede on a set play like that. We had chances with Luka and Rafa to score, but ran out of steam and Cristante got the third.”
Not a good year for Milan
Asked to assess his work since taking charge, Conceicao insists there's plenty of blame to be shared over a poor season for the Rossonero.
He also said: “Everyone has to evaluate what he did in his work. I am very demanding with myself, before the game I looked up the statistics and since I arrived, we earned enough points to get into the Champions League zone.
“I am not saying it was a good season or perfect five months, absolutely not, but there were some positives too. We won the Supercoppa Italiana, we reached the Coppa Italia Final, but when it came to the key games, there were negative moments.
"This is not a good year for an historic club like Milan, everyone has to evaluate his work and then talk it over at the end.”