Defeat at Napoli means their destiny is out of their hands ahead of must-win game with Bayern Munich
Manchester City's qualification hopes hang by a thread
Two goals from Edison Cavani, who had not scored since October 29, secured a 2-1 win for Napoli who can now advance from Group A to the next phase, at the expense of City, owned by Sheikh Mansour bin Zayed, if they win away at Villarreal.
Bayern Munich lead Group A with 13 points after beating Villarreal 3-1 and City need to beat Bayern at home and hope Napoli do not win in Spain.
"You never know. We'll see what happens," said Mancini. "We didn't deserve to lose, but in the Champions League you can't allow your opponent certain types of chances. Napoli is a sneaky Italian side. We had our chances and it just didn't go in.
"I'm upset over the result but not anything else. I was pleased with our performance. But we conceded two goals that we shouldn't have allowed."
Mancini said there was "no explanation" for the difference between City's results in the Premier League - having beaten Manchester United 6-1 last month - and in Europe.
"This is a strong that plays good football and plays to win but occasionally you can lose matches, especially in the Champions League," he said. "I'm not angry and I'm not disappointed. This can help us grow."
Italy forward Mario Balotelli had equalised for City in the 33rd minute but Cavani restored Napoli's lead in the 49th and Marek Hamsik hit the post in the 76th for the home side. Yet City could have salvage at least had Balotelli converted one of four chances to equalise.
"We still haven't done anything," said Napoli manager Walter Mazzarri. "We've got to go beat Villarreal in Spain, and don't think that's going to be easy. But let's enjoy this for now. Advancing in this group would be a real achievement. You've got to remember that Napoli hasn't won matches at this level for 21 years.
"Let's enjoy this beautiful moment. We knew we could do it from the very first day," Cavani said. "We always prepare to give our maximum and today we were at our best."
City's equaliser was the product of a poor clearing attempt from Salvatore Aronica. The ball went directly to David Silva, whose shot was deflected by goalkeeper Morgan De Sanctis directly to Balotelli, who sent it into an empty net.
"(Aronica) made a mistake but otherwise he played great," Mazzarri said. "You've got to remember that most of this squad is playing the Champions League for the first time and this was only our fifth match."
Balotelli was playing his first club match back in his home country since leaving Inter Milan and he now has two Champions League goals to go with his six Premier League scores this campaign.
Mancini revealed that Balotelli had a fever Monday, but said he felt better before the match.
The scene at the San Paolo stadium was electric, with about 60,000 fans filling the stands for one of the biggest crowds since Diego Maradona led Napoli to Italian titles in 1987 and 1990.
However, there were only a couple of thousand City fans, leaving the visiting supporters cage - which features double sets of Plexiglass barriers and netting stretching up to the stadium roof - half empty.
Before kickoff, Napoli fans put on a fancy display, as fans held up cards in the squad's blue-and-white colors nearly all the way around the main ring of stands, and formed the outline of the letter 'N' with lines of flares on one end.
During the second half, fans held aloft a banner mourning the recent death of Maradona's mother, Dalma Salvadora Franco de Maradona. It read, "Lay in peace the mother of football, ciao Dona Tota."