Peter Rasmussen disallowed a late effort from Sergio Aguero which incensed Mancini and City's volatile Italian forward Mario Balotelli also had to be restrained by team-mates at the end of the match after his late penalty appeal was turned down.
"I said to the referee 'It was a goal, congratulations, it was a goal,'" Italian Mancini said after the enthralling Group C clash at the Etihad Stadium. "I didn't see Mario's penalty [appeal] but the players said it was a penalty.
"I didn't see the late situation with Mario but the referee and his staff were really poor tonight. I think we scored three goals tonight, but we conceded two stupid goals."
The draw kept alive City's faint hopes of reaching the next stage but they need to win their final two games, at home to Real Madrid and at Borussia Dortmund, while hoping other results go their way - a chain of events Mancini believes is impossible.
"There is no chance," he said. "We can only get eight points. If we finish with eight points and go through, then we can win the Champions League because this will be our destiny.
"If we win our next two games and go to the second stage then it is our destiny to win the Champions League.
"I always believe in my team. Sometimes, we make mistakes, like when we conceded two goals today, but I always believe in my team," he added.
DISAPPOINTED DE BOER
Ajax coach Frank de Boer was disappointed for his players, who could have moved closer to at least ensuring they stayed in European competition via the Europa League with a victory.
"It's a good sign that the players are disappointed in the dressing room after the game because they had the feeling we could make a big step forward to the next phase, in the Europa League or the Champions League, and put City behind us," he said.
"Playing in Europe is important, no matter whether the Champions League or the Europa League, but obviously we will try and get a result against Dortmund so it is the Champions League."
De Boer had a different view to City about the contentious late decisions.
"I thought immediately it [Aguero's effort] was offside then I looked at the referee and the assistant referee and they were very confident there was no doubt about it," he said.
"I could not see [the penalty appeal] from the bench but sometimes you have some luck with referees, sometimes you have bad luck."
