With Manchester United and Chelsea slumping to home defeats the previous day and Tottenham Hotspur managing only a draw, City arrived at the Stadium of Light intending to make the chasing pack pay for dropping points.
Instead, they too were shocked as Ji Dong-won slotted home in the third minute of stoppage-time to snatch the three points for the hosts after a frantic finale when City had desperately chased a winner of their own.
"A team like us can't concede a goal on the counter-attack at the end," Mancini told Sky Sports after his side's second league defeat of the season.
"It was offside and we can't do anything about it."
The visitors made six changes from the side that drew 0-0 at West Bromwich Albion on December 26, Mancini having an eye on Tuesday's match at home to Liverpool, and lacked a cutting edge in the first half as an overcrowded midfield stifled both teams.
City's best chance came shortly before half-time when Edin Dzeko skimmed the top of the bar. Earlier, Sunderland saw Hart rush forward to force Nicklas Bendtner wide when the forward was through on goal.
With the clock ticking down, City threw players forward and could have snatched it when Silva's shot was pushed by keeper Simon Mignolet into the path of Micah Richards whose header bounced on to the bar before being cleared.
Sessegnon's through pass found substitute Ji who kept his nerve to slot the ball into an empty net with the last kick of the game.
The win lifted Sunderland to 13th place as their revival since Martin O'Neill took over as manager last month continued.
"We knew we were going to have to withstand ferocious pressure from Manchester City. We did it and we did it remarkably well," said O'Neill who took over with the club in 16th position.
