Former City winger Adam Johnson came back to haunt the reigning champions with a 53rd minute winner at the Stadium of Light which left Mancini's men seven points behind league leaders Manchester United.
City have not been themselves in front of goal recently with just nine goals in their past seven matches and Mancini has urged them to improve their output in front of goal if they are to challenge for another title.
"We deserved to win this game. We had a lot of chances, we played well, but we didn't score," the Italian said.
"This is our problem, we don't score, we don't score enough goals to win the game.
"Last year, we scored one, two, three goals every game. Now when we have chances, we are too soft and this is not good.
"We are too soft in attack, too soft when we have chances, too soft when we shoot. Sometimes we don't shoot, we want to have one touch more. This is not good."