The Italian was angered by Joe Bennett's tackle on Gareth Barry, prompting Mancini to enquire as to a possible punishment - a move that irked Lambert.
"I didn't say anything to him [Lambert]," Mancini told reporters. "There are some managers it is better to shut up."
"I asked the fourth official if there was a yellow card, without moving my hands, and he comes over to me.
"I can understand if I was talking to him but I didn't say anything.
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"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."
After being told what Mancini had said regarding their clash, Lambert replied: "If that’s what he said [that he was just talking to the fourth official] then fine, I respect him as a manager and as an ex-player. I don’t have a problem [with him]."
The hosts twice got themselves in front only to be pulled level on both occasions, before extra time goals from Gabriel Agbonlahor and Charles N'Zogbia gave the Villans a shock win.
Mancini had recently seen his side surrender a lead late on against Real Madrid in the Champions League and underlined his concern at the worrying trend.
"This [conceding goals and throwing away leads] is a problem, we need to work with our defenders because they are not working well at this moment," he told reporters.
"I am disappointed for the result. I think it was a difficult match because Aston Villa are a good team, we didn’t play well. We had one unlucky moment because we had chance to score but conceded a goal.
"I think we made some mistakes with their goals, but at the end of the day they deserved to go through. We didn’t play well, and our play is not quick. We want to take a touch more everytime."
Lambert on the other hand was delighted with the victory, saying: "It’s a massive result for us, really huge.
"I think we never deserved to go a goal behind but we did well to come from behind, not just once but twice and to go and win the game is a huge effort for us. I’m delighted with the way we played."