Allegri was furious after the 1-1 draw with Catania on Saturday, suggesting Marotta "ought to shut up" for continuing to complain about refereeing errors.
"Allegri is a very good Coach, but I do not respond to opposition tacticians," Marotta told Sky Sport Italia.
"I do not want to fuel more controversy. I think Robinho's goal should've stood, but this requires new technology and not just having extra officials on the line. The more errors are reduced, the better football will be.
"If Milan put in a formal request for goalline sensors to be used in Serie A next season, then we will be by their side."