The club have issued a ban on attending future matches to one fan and registered a complaint with Merseyside Police about his conduct.
The contest between the Blues and the French club boiled over when captain for the night, Ashley Williams, barged over goalkeeper Anthony Lopes prompting angry reactions from Lyon players.
A number of players from both sides became embroiled in a shoving match that came to blows at one point up against the advertising hoardings by the Gwladys Street stand. Television replays showed some fans getting involved including one who left his seat with a small child in his arms to aim a punch at one of the opposition players.
Everton's statement read as follows:
Club Officials have reviewed the footage of an incident that occurred in the 64th minute of the game against Olympique Lyonnais where supporters towards the front of the lower Gwladys Street End became involved in a confrontation between players.
We have identified one individual whom action will now be taken against. This will include a ban from attending future Everton fixtures and the Club registering a formal complaint with Merseyside Police.
Meanwhile, Uefa have opened disciplinary proceedings over the incident and will likely fine Everton for "aggression by supporters" towards players. Their decision will come down on 16th November.