Inter conceded two Miralem Pjanic goals in the final half an hour as second-placed Roma ran out 4-2 victors in Serie A action at the Stadio Olimpico.
Mancini, who lost for the first time since replacing Walter Mazzarri ahead of the Milan derby last week, was sent to the stands following Roma's third goal on the hour-mark.
However, the Italian boss was left to lament errors that saw his team slip to 11th in the top flight.
"Just look at the game... I honestly don't want to waste words on the referee. I don't care. I protested, but it wasn't a protest about nothing," Mancini told Sky Sport Italia.
"Roma have been playing very well since last year, so we knew it would be difficult, but we were in it up to a certain point and that is important.
"We made mistakes, as they were able to cut in from the right too often and we wasted some chances. We did good and bad things tonight, so we have to work.
"These are quality players and you can't leave them space to play. We were too slow closing them down."
Inter are six points adrift of the UEFA Champions League play-off spot after 13 matches but Mancini has not given up hope of qualifying for the illustrious competition.
"We cannot achieve everything in a few months. We'll try to do the best we can and would certainly aim to qualify for the Champions League with two different paths to that," said the former Manchester City manager.
"This team was built to play with a different system and different coach in Mazzarri, so we are missing players in certain positions and need time to adapt. We have a month until the Christmas break and need to do all we can in this time."
