The leaders showed were susceptible at the Stadium of Light as Sunderland survived a battering before snatching victory deep into injury time. Substitute Ji Dong-won made the most of a counter-attack as too many men in blue stood and watched, and the chance to establish a gap over rivals Manchester United evaporated.
Asked if that was good enough, Mancini replied: "No, not for a top team. In that situation, we attacked with eight players and the same players who attack need to come back and run quickly."
He added: "I know football and for that reason in the last 15 minutes, I continued to call [central defenders] Vinny [Vincent Kompany] and [Joleon] Lescott to say, 'Stay there, stay there, don't leave the space', because that was dangerous.
"We continued to attack and sometimes we wanted to attack with 10 players. This is impossible. But that's it, it's finished. We have a game in 48 hours and we need to recover now."
There was a suspicion of offside about the goal, although after seeing his side concede a controversial penalty on Boxing Day, Sunderland boss Martin O'Neill was delighted to have received the benefit of the doubt.
O'Neill said: "They tell me it was marginally offside - marginally, marginally - and we ended up winning the game. It's been an incredible weekend for teams and we are delighted with three points."
Mancini, who headed down the tunnel before the final whistle, admitted his side had been made to pay for missed chances.
He said: "It's frustrating because we can't lose a game like today's. In the second half, we had I don't know how many chances to score. But football is this. Sometimes you can't win. Sometimes you score three or four goals in a game, sometimes you can't score even if you have 10 chances to score.
"I am disappointed that we conceded a goal because a strong team cannot concede a goal like this."