Mancini was up in arms that Maynor Figueroa, having completely misjudged the bounce of Nigel de Jong's long punt forward, only got a yellow card for handling the ball to prevent Sergio Aguero running through on goal from the halfway line.
Watching on TV, Rooney was quick to make a sarcastic comment. "Was Manchini (sic) asking for red card????" he wrote on Twitter. Martinez said: "He has misjudged the bounce but he is not even in his own half. I don't think it is a red card. I've been here long enough to understand that trying to influence the referee is not accepted in the British game."
Edin Dzeko broke an 11-match scoring drought to give City the points at the DW Stadium.
However, the red card row was the major talking point following City's FA Cup defeat to Manchester United nine days ago, when Mancini lambasted Rooney for his part in getting Vincent Kompany sent off.
Then, three days later, Mancini got involved in a tunnel row with Liverpool's Steven Gerrard, who accused the Italian of doing exactly the same thing following Glen Johnson's two-footed tackle on Joleon Lescott.
Mancini defended his latest actions, saying: "It is normal when it is something like today. I am on the bench. It is different to a player who is near the referee. They can have more influence. From the bench, it is what you think at that moment but the referee doesn't see you."
Meanwhile, Martinez predicted the title race will go down to the wire after City's win took them three points clear of Manchester United and five ahead of Tottenham, who visit the Etihad Stadium on Sunday.
But, while Martinez conceded the Blues are favourites to finish champions for the first time since 1968, he believes it will be a closely-fought contest.
"Quite clearly Manchester City are favourites," he said. "At this stage of the season, when you are top, you have to be favourites. But we all know the competition is going to be ferocious until the end of the season. It is probably going to be one of the tightest of the last few seasons."