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.
In 2011, Mancini was involved in a row with then Fulham manager Mark Hughes, the man he replaced at City in December 2009, over an end-of-match handshake, where the Welshman said the Italian had not looked him in the eye.
Mancini said Hughes had failed to shake his hand properly the previous year.
In 2010, Mancini was handed a suspended 20,000 pound fine for barging into Everton manager David Moyes, having accused his rival of wasting time by holding on to the ball.
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."
League champions City, four points behind leaders Chelsea after five games, are next in action at Fulham on Saturday.
