The Italian exchanged words with Villa counterpart Paul Lambert following a heavy tackle on Manchester City midfielder Gareth Barry by Joe Bennett in the 4-2 extra-time defeat.
"I only asked the fourth official if there was a yellow card, without moving my hands, and he [Lambert] comes over to me," Mancini told British media.
"I am very tired with their behaviour. Sometimes these managers go to the big stadiums, and the other manager says everything and they say nothing.
"When they go to [Old] Trafford, they say nothing. When other managers talk about the referee they always sit on the bench. I don't like this type of behaviour," he added in reference to city rival Manchester United's ground.
Mancini and United boss Sir Alex Ferguson had to be separated in April after a touchline spat during City's 1-0 Premier League win that helped deliver the club's first top-flight title for 44 years.
By contrast, Lambert spoke highly of the former Sampdoria and Italy player, admitting the disagreement was "nothing."
"I respect him as a manager and an ex-player. It wasn't really a spat. It was nothing."
