"I think we deserved to win, especially in the second half. Considering the overall play and number of chances, Roma did enough for the victory," Spalletti.
"Both teams were a little rusty in the first period and we both had scoring opportunities, but they are a more physical side and made the most of the set play.
"After the break I tried to fire up the players, who were a little anxious at the atmosphere and making their debuts.
"You could see then that there were players who had character and could entertain the fans, as the pressure of getting a result was not weighing on their shoulders."
Amantino Mancini was jeered by some of the Giallorossi fans, but he scored the goal that prevented Manchester United winning all six group games.
"I have great faith in Amantino, probably more than most considering the number of big games I have started him in. He played a good game and was unlucky in the first half, but could have tried to take on defenders one-on-one a little more.
"Antunes probably felt the anxiety less than others, but he didn't show all the extraordinary quality he has in that right foot."
Spalletti also revealed a bet he had with colleague Sir Alex Ferguson.
"As soon as Ferguson finishes the interviews, we will meet to exchange a bottle of Chianti I promised him."