The pair exchanged heated words in the second half of City's 4-2 Capital One Cup defeat at the Etihad Stadium after the Italian complained to the fourth official about a tackle by Joe Bennett on Gareth Barry.
Mancini, who has had his fair share of touchline confrontations during his time in England, said Premier League managers do not treat him the same way they treat Sir Alex Ferguson and expressed his unhappiness with Lambert's conduct.
"I am tired with this manager because I didn't say anything," he said.
"I asked the fourth official if it was a yellow card without moving my hands. He [Lambert] comes up to me every time but after this some managers go to bigger stadiums and don't say anything.
"I am tired of this, very tired. I am tired with their behaviour and it's better that some managers shut up because I didn't speak with this manager.
"I asked the fourth official if it was a yellow card and I thought the referee had left his yellow cards in the dressing room.
"Every time I say something, they come. After, when they go to Old Trafford, they never say anything. When other managers [at Old Trafford] talk against the referee, they always stay on the bench and say nothing.
"I don't know why. Maybe it's because I am Italian but I don't know the reason. There's no problem. I just don't like this type of behaviour."
Mancini and United boss 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 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."
City twice threw away a lead given to them by Mario Balotelli and then Aleksandar Kolarov - after Villa old boy Barry's own goal had got the visitors back in it.
Gabriel Agbonlahor took the tie to extra time and added a second late on after Charles N'Zogbia had put Villa ahead for the first time.
"It was a difficult match because Aston Villa were a good team," said Mancini. "We didn't play well and we had some unlucky moments but I think they deserved to go through.
"We are so disappointed. We didn't play well and our play is not quick, we want one touch more every time and this is no good.
"It is the fourth competition but it is the only competition we didn't win and for that reason we wanted to stay in this cup because in two years we have won everything and are missing this one."