City went down by the only goal 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 insisted his men had only themselves to blame after not making the most of the chances they created before succumbing to former team-mate Adam Johnson's 53rd-minute strike.
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."
Defeat at Sunderland, coupled with United's home victory over Newcastle, saw Sir Alex Ferguson's men reach the halfway stage of the Premier League season with a commanding lead, but one the Italian is confident is far from decisive.
He said after the 1-0 loss: "It hasn't changed. At this moment, United are better than us, they are at the top, but we have time to recover.
"We need to resolve our problems before and after, maybe we can win. It's no problem, seven points.
"That's not important. We know United are a fantastic team and probably they will win every game, but the season is long and it is not important if it is six or seven or four points."
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."
Watch: Sunderland stun Manchester City... More Videos
Mancini refused to criticise Hart for his part in the goal despite the keeper appearing to have moved too far to his right to get back across in time to repel Johnson's effort.
He said: "Johnson was really clever because Joe thought that Johnson was going to cross and instead, he shot.
"He did very well, Johnson."
Opposite number Martin O'Neill, however, was not in the slightest bit interested in Mancini's view.
He said: "Honestly, I am really not particularly bothered, I am genuinely not bothered about what Roberto Mancini would say about the team.
"I have seen it before with other managers. I'm not bothered. I thought we were terrific today [Wednesday]."
The game was settled by Johnson's second-half effort, but it was one which left Mancini with more than one cause for complaint.
Both he and Pablo Zabaleta were convinced City should have been awarded a free-kick for Craig Gardner's challenge on the full-back during the build-up, although referee Kevin Friend did not agree.
Sunderland played on and when Carlos Cuellar fed the ball out to Johnson, he cut inside before blasting a long-range shot past keeper Joe Hart, who was caught flat-footed and allowed the ball to squirm past him.
Johnson initially thought his former team-mate had kept his effort out, but his joy was unbridled as it dawned on him that the ball had indeed ended up in the back of the net.
Mancini, who rather surprisingly absolved Hart of blame for the goal, was scathing when asked for his view of the official's decision to allow play to continue.
He said: "The referee ate too much for Christmas. He was not in good form. He and the linesman, I think, after Christmas, it can happen to have a bad performance like today."
City had earlier hit the bar through skipper Vincent Kompany and Sunderland goalkeeper Simon Mignolet had to make three fine saves from Yaya Toure, David Silva and later Sergio Aguero as the visitors launched a late, but ultimately unsuccessful fightback.
Asked if the performance was Sunderland's best of the season, 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, and we did both of those very well.
"And yet we were able to carve out some great chances in the game."
O'Neill was understandably thrilled with a third win in four Barclays Premier League outings and with the return to form of Republic of Ireland winger James McClean in particular.
O'Neill said: "James McClean was truly terrific, offensively and defensively. He is getting back to that sort of form.
"He has had a pretty difficult time because everybody was telling him about the second season syndrome and of course full-backs are closing him down a lot more quickly now and not giving him the sort of space he probably enjoyed this time last year, for instance, and he has had to try to cope with that.
"He's attempted to do that and he was great."