City went down by the only goal of the game for the third successive season at the Stadium of Light, while their neighbours came from behind three times to defeat Newcastle 4-3 at Old Trafford to extend their lead at the top.
Mancini said: "We deserved to win this game. We had a lot of chances, we played well, but we didn't score. 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."
The Black Cats, who took four points from City last season and were the only side to leave the Etihad Stadium with something to show for their efforts, defended resolutely to ensure Johnson's contribution was decisive, but Mancini was less than gracious in his assessment of the game.
He said: "I think they (Sunderland) are really lucky against us at home because you can't create every time 15, 20 chances like this year, last year, two years ago and in the end, you lose the game.
"They are very lucky against us. They defend well, but we need to be stronger when we have a chance to score."
Mancini was also scathing when asked for his view of referee Kevin Friend's decision to allow play to continue in the build-up to the goal, when the manager believed a foul on Pablo Zabaleta was missed. He added: "The referee ate too much for Christmas. He was not in good form. He and the linesman."
Asked if the performance was Sunderland's best of the season, manager Martin O'Neill said: "Considering the opposition, I would have to say yes. We gained a bit of confidence form winning against Southampton and took that into the game, but we knew there would be times when we would have to play without the ball and we would have to defend strongly."