The pair exchanged heated words in the second half of City's 4-2 defeat after the Italian complained to the fourth official about a tackle by Joe Bennett on Gareth Barry.
"I am tired with these managers," said Mancini, who has had his fair share of touchline confrontations during his time in England.
"I didn't say nothing to him (Lambert). There are some managers it is better to shut up.
"I asked only if there was a yellow card - without moving my hands (Mancini has been guilty in the past of waving imaginary cards) - with the fourth official and he comes over to me.
"I didn't speak with him. I asked the fourth official if it was a yellow card because I thought the referee had forgotten his yellow cards in the dressing room.
"I don't know what is the reason. I can understand if I was talking to him but I didn't say nothing."
Mancini added: "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."