European governing body UEFA have confirmed that the incident was not reported by either referee Peter Rasmussen or their match delegate at the Etihad Stadium.
Mancini came onto the field after a stormy final few minutes in which Sergio Aguero had a goal disallowed and Mario Balotelli had a penalty appeal turned down.
A UEFA spokesperson said: "Nothing was reported neither by the delegate nor by the referee. No disciplinary proceedings are opened."
City had fought back from 2-0 down to 2-2 and thought they had snatched the lead in the 88th minute when Aguero turned home from close range.
But celebrations were cut short as a flag had been raised against Aleksandar Kolarov for straying marginally offside before crossing for the Argentinian.
In a frantic finish, Balotelli went down in the area after being pulled back by Ricardo van Rhijn in injury time but Danish official Rasmussen blew the final whistle.
Balotelli protested to Rasmussen and eventually needed to be pushed away by captain Vincent Kompany while Mancini remonstrated about the disallowed Aguero goal.
"I said it was a goal," said Mancini, when asked after the game what he had said to Rasmussen.
"I didn't see the last situation with Mario that was a penalty. I said it was a goal.
"The referee and his staff were really poor."
There were fears Mancini could face a touchline ban for his actions but he will be able to conduct duties as normal for City's final two Group D matches against Real Madrid and Borussia Dortmund.
City will need to win both of those matches to stand any chance of reaching the knockout stages after their latest damaging result.
Mancini's man have just two points from four games and other results will need to go in their favour for them to avoid premature elimination for a second successive season.
The Italian said: "Unfortunately we took only one point and now I think it is finished for the Champions League."
City had seen the visit of Ajax as a must-win encounter but their hopes were badly damaged as they conceded twice to Siem de Jong from corners inside the opening 17 minutes.
Yaya Toure replied with a superb volley after 25 minutes but despite Aguero's leveller 16 minutes from time and plenty of attacking intent, City could not force themselves in front.
Aguero, who twice slipped when well placed on the wet surface, was also denied by an offside flag early in the second half while Balotelli forced Kenneth Vermeer to save with a firm header.
Amid the chaos at the end of the game, Mancini also clashed with a TV cameraman but the manager said he reacted angrily because he did not want to be filmed.
Mancini said: "The camera wanted to film me after the game. I said, 'Finish, finish. Do not film me'."