City left the Stadium of Light pointless after Darren Bent scored from the penalty spot in the fourth minute of stoppage time to give the hosts a 1-0 win.
"We played very well in the first half," Mancini told Sky Sports after the match.
"We had three or four chances in the first half to score and an incredible situation (the Tevez miss), but that's football, it's strange.
"It can happen, but we had two or three other chances to score.
"Second half we didn't play very well and a penalty after the 90th minute - that's football.
"I think this game was very difficult and if you have chances to score a goal, you score.
"If you play as well as we did in the first half then you must win the game. After that, the game changed.
"It's a blow today, sure," he added. "The start to the season, we've played very well and played as a team.
"First half today we played some fantastic football. I think we found that many times they defended with 10 players without the ball and we must pass the ball to find a solution.
"I hope that it can make a difference for us today because now we know that every game will be very difficult."