Dimitri Payet scored twice as Marseille defeated its rival 2-1 on Monday (AEDT), although the opening goal came from the penalty spot amid much controversy.
Lyon midfielder Thiago Mendes was punished for handball inside the area, yet replays appeared to show Marseille's Morgan Sanson had also handled earlier in the move.
Aulas later criticised the VAR decision, also referring to a clash between Dario Benedetto and Leo Dubois, prompting a response from Marseille on Wednesday.
While "surprised" Aulas, who holds a role on the executive committee at the French Football Federation (FFF), had questioned officials, they offered ideas for how VAR could be better implemented in the league.
In a lengthy statement, Marseille suggested they join with the FFF to approach refereeing body the International Football Association Board, with their plan to install a microphone on referees to broadcast live the exchanges between the official and players, as well as broadcasting such conversations on a slight time delay.
They also advocated slow-motion replays being aired inside the stadium "in such a way as to show the public that the picture does not explain everything", plus a report be published after each day of the championship "specifying the right refereeing decisions, the obviously erroneous decisions and the decisions that should have been made but which were not".
Marseille pointed to the successful implementation of similar systems in both rugby and the NBA.
They described the increased "transparency" of such processes, adding they would "prove that these mistakes affect all clubs equally in the long run".
In addition to Aulas' comments regarding decisions on the field, Marseille also responded to criticism of the atmosphere at their ground, where Lyon's bus was attacked as it arrived at the venue.
Lyon had been advised to use an unmarked bus, as Marseille do against Paris Saint-Germain, but chose instead to arrive in club colours.
"The match was marked in the stadium by the exemplary behaviour of the immense majority of our supporters who, with their tifos and their encouragements throughout the match, gave the most beautiful expression of support to their club," the statement read.
"The Velodrome - with a record Ligue 1 attendance - showed again a unique atmosphere in France and Europe. The show on the field and in the stands ensured our championship an exceptional promotion around the world."