Mourinho claimed he would not have been able to return to the Spanish capital had his Real side suffered the same European fate as Mancini's Barclays Premier League champions.
Madrid ended City's hopes of reaching the Champions League knockout phase after drawing 1-1 at the Etihad Stadium on Wednesday.
The pair have a perceived rivalry dating back to when Mourinho succeeded Mancini as Inter Milan boss in 2008.
Mancini said: "Mourinho is not my chairman, he is not my owner. What Mourinho said is not interesting.
"Mourinho wants to talk about everything and for me it is not important."
Mourinho had spiced up the contest the night before by saying City would be eliminated regardless of the result and, given all their talent, that would hurt them greatly.
That was also interpreted in some quarters as an attack on Mancini as it could have suggested the manager was not making the most of the players at his disposal.
Mancini has not wanted to get dragged into a war of words and said nothing should be read into him not shaking Mourinho's hand after the game.
He said: "I didn't see him after the game. Before the game, yes, after, no."
Mancini has benefited from the huge financial backing of Sheikh Mansour in his team-building at the Etihad Stadium and has delivered by winning an FA Cup and a Premier League title.
It was suggested to him that negative remarks from other managers could reflect an envy from their part of Mancini's position.
"I don't know," Mancini said. "Sometimes it could be.
"I am here, but I will not stay here for 20 years. Other managers will have time to come to Manchester City, but in this moment I am here and we are working well.
"I don't know why sometimes they talk about us."
City could still maintain an interest in European competition by securing a consolation place in the Europa League.
Given the reduced status of that tournament, Mancini accepts that could be a mixed blessing, but on the whole he would like to grasp the opportunity to win more silverware.
When asked if City might succeed better without the additional fixtures, Mancini said: "On the one hand, probably yes, but on the other the Europa League is also another trophy for Manchester City. For Manchester City to win a trophy is important.
"If it is not Champions League it could be Europa League. We will see but we play a difficult game in Dortmund. It will not be easy."