City squandered the chance to open up a three-point lead at the top of the Barclays Premier League as they conceded at injury-time goal at the Stadium of Light on Sunday.
The defeat compounded the frustration felt after a goalless draw at West Brom on Boxing Day and there is little time to dwell as Liverpool visit the Etihad Stadium on Tuesday.
Mancini said: "We missed a big opportunity, a big chance to go three points up on (Manchester) United.
"I thought we threw three important points out of the window.
"It was important but now it is finished and we can do nothing.
"But at the same time, when we arrive back in Manchester, we need to think positively for the next game and for the future.
"We play again quickly and we should have good concentration for the next game.
"We have 45 points and we have scored 53 goals, and I think we need another 45 points in the second half."
City were pushing for a late winner when they were caught on the counter-attack and Black Cats substitute Ji Dong-won broke through in dramatic fashion to beat Joe Hart.
The visitors had dominated possession in the second half and were unlucky in that Ji was marginally offside when he received the ball for the decisive touch.
Yet Mancini was alarmed at how vulnerable his side had seemed at the back throughout the game and wants improvement.
He said: "I don't know how many chances we had to score but we need to pay attention in situations where we concede three or four counter-attacks.
"A top team can't concede situations like this - maybe one, but not three or four.
"We wanted to try to score but sometimes, when you are on the pitch, you need to understand that there are some games you cannot score. You can do nothing.
"In that moment we should stay and finish - one point is better than nil."
Mancini has voiced his unhappiness with City's new year schedule, the Liverpool game kicking off little over 48 hours after the final whistle on Wearside.
Because of that Mancini made six changes on Sunday with key men David Silva and Sergio Aguero left on the bench and Mario Balotelli not risked due to an ankle problem.
The line-up is expected to change again for the Liverpool clash.
Mancini said: "I changed six or seven players because I trust all my players, and also if I change six, seven players, they know what they should do on the pitch.
"Because we play two games in 48 hours, it's impossible to play the same players."
Liverpool frustrated then unbeaten City as they held them to a 1-1 draw at Anfield in November.
Since then Liverpool have had some disappointing results of their own but they impressed in a 3-1 defeat of Newcastle last Friday.
Mancini said: "They are in good form, but all the teams are in good form.
"We are in an unlucky moment, but things can change in two days."
Midfielder Nigel de Jong made his first start since November at Sunderland and was removed at half-time.
The Dutchman, who had a spell out in August and September with a foot injury, has fallen down the pecking order this season but Mancini insists he remains central to his plans.
Mancini said: "Nigel had too many problems when we started the season, two months off for injury.
"After this the squad played a different system with two strikers, two offensive players like wingers and only two midfielders.
"For this reason Nigel did not play a lot of games but he is still an important player. There is no change in this situation. Now he can play.
"I think it is normal that one player, when he doesn't play, is frustrated.
"For him it is difficult but now we are playing five games in 16 days and we need our players."