Marquez and Rossi had collided on track during the race, an incident for which the Spaniard received a 30-second penalty.
The pair then exchanged heated words after the race as Marquez went into the Yamaha garage and claimed he just wanted to apologize.
Rossi reacted angrily to his presence and now Miller believes the two experienced men, who have 11 world titles combined, should know better than to let their rivalry affect their races.
“All of us here are racing and risking our lives and I think it’s pretty silly and immature that these fans and drivers are fighting each other,” Miller said.
“They are quite old and need to remember that life is short and we are risking our lives here.
“I’ve seen how this situation developed with a lot of people and people choosing sides and I just want to refresh people’s memories of Marco Simoncelli and Dani Pedrosa and how that ended.”
Pedrosa and Simoncelli were paddock rivals with a bitter relationship that culminated in a crash caused by the latter’s overly aggressive overtaking at the 2011 French Grand Prix.
Pedrosa, chasing a world title after three consecutive podium finishes, broke his collarbone and missed the next three races, unable to challenge eventual winner Casey Stoner.
And while the fight between Rossi and Marquez has yet to result in a series injury, Miller has urged MotoGP authorities to step in or the two riders to rein in.
“I think they need to control the paddock fights a bit better,” added Miller.
“We’re here to bike race and we’re here to fight, but the fight in general should try to stay on track and not try to fight so much in the media.
“I think that’s one of the clearest things. There are a lot of people coming, especially the journalists, who come up to you and try to get you to say something to screw it up, and I don’t think it’s the right way.
“I think the fights should be left more to the side and of course we drivers have to be careful what we say because words can be twisted as we have seen many times.”