City were pushing for a winner right until the end of the Premier League clash at the Stadium of Light, but in the 93rd minute the hosts scored with the last kick of the game when Ji Dong-won finished off a counter-attack.
Mancini's men stay top of the league on goal difference despite the loss but have missed a golden opportunity to widen the gap after main rivals Manchester United lost to Blackburn Rovers on Saturday, and the Italian was disappointed with his side's failure to score for the second game in a row.
The 47-year-old told reporters: "It was frustrating because we can’t lose a game like we did today. The second half we had I don’t know how many chances to score but in football sometimes you can’t win.
"I made a lot of changes but we did well. In the first half we played so-so but in the second half we played very well. We have now been unlucky in two games because we had lots of chances to score. But football is like this. Sometimes you score three or four goals every game and sometimes you make 10 chances and don’t score."
The boss then moved on to criticising his own defence for conceding a goal on the counter-attack, suggesting that he had to continually shout at his defenders in order to position them correctly while the rest of the team searched for a goal.
He continued: "I am disappointed that we conceded the goal because a strong team cannot concede a goal like this, because we conceded a goal on a counter-attack which is very dangerous.
"I know football and for this reason in the last 15 minutes I continued to call Vinny [Kompany] and [Joleon] Lescott and Kompany to say ‘stay there, stay there’ and don’t leave this space and I think I nearly lost my voice because of this.
"I understood that it was dangerous because we continued to attack and at the same time we wanted to attack with 10 players and this is impossible.
"In that situation we attacked with eight players and the same players that were in attack we needed to come back and run quickly.
"I have been saying in press conferences that now we are scoring three or four goals a game but there will be times when we don’t score any goals because football is like this. There are times when you can’t score and you don’t know why.
"I don’t know how many chances we had today. I am not worried about the fact we didn't break them down. I am worried because I think that sometimes on the pitch I need some players that understand the situation and don’t leave two defenders alone when we concede a counter-attack. It can’t happen in a strong team. We need to improve this situation."
With Mario Balotelli again making headlines for the wrong reasons, the striker was not included in the squad, but his manager insisted the player was injured and focused talk on his side's display.
He added: "Balotelli? He had a problem in the training session yesterday with his ankle and for this reason was in the stands. I hope he will be okay for Liverpool.
"I hope that my players can understand that we are a top team and we can’t concede a goal like that.
"I was really disappointed."
Mancini's side are next in action when they take on Liverpool at the Etihad Stadium in the Premier League on Tuesday night.
How do you stay up with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.