Referee Peter Walton sent both managers to the stands and the Football Association is now studying Walton's report before deciding on any action against Mancini and Moyes.
Related ArticlesMancini made a mistake picking on MoyesManchester City v Wigan: previewMancini vs MoyesRoberto Mancini: I was unfairly sent offMancini and Moyes play down touchline bust-upSport on televisionMancini attempted to defuse the situation by apologising personally to Moyes after the game but, despite the flashpoint, City defender Vincent Kompany believes that the Italian's actions only highlight his determination to succeed at Eastlands.
Kompany said: "Everyone at this club is passionate and wants to bring success, so there will be times when emotion takes over.
"The boss showed how much he cares and I don't see a problem with what he did. We were losing and he wanted to get the ball back in play. That was all there was to it. Too much has been made of it."
City's defeat against Everton has hit the club's hopes of qualifying for the Champions League by claiming fourth place in the Premier League.
But the Belgian defender insists that Monday's home game against Wigan offers Mancini's team the perfect opportunity to re-establish their credentials.
Kompany said: "Of course it would have been nice to have won and gone into fourth spot, but overall I don't think it makes a massive difference.
"We still have to play Tottenham and Aston Villa at home and, though they will be difficult games, I think it is a positive that they have to come to our ground.
"Villa lost points on Wednesday and Liverpool and Spurs will probably drop more points in the remaining games, but nobody is going to give up trying to get that fourth spot and it could well go to the last game of the season.
"We've only lost once at home all season so we are confident that we can get back to winning ways very quickly and our destiny is still in our own hands."