Caen began their Coupe de la Ligue campaign with a 1-0 victory away to Ligue 2 side Lorient.
The LFP has fined Paris Saint-Germain and threatened the French champions with a potential supporters' ban because of the damage caused to Parc OL.
Paris Saint-Germain have "accepted with great difficulty" a ban on their travelling supporters for the Ligue 1 trips to face Angers and Metz.
Seats at Lyon's stadium, the venue for the showpiece match, were ripped up, toilets were smashed and anti-Lyon graffiti was daubed on walls.
PSG midfielder Marco Verratti was delighted his team answered their critics with their 4-1 win over Monaco in the Coupe de la Ligue final on Saturday.
PSG proved to be too strong for Monaco in Saturday's Coupe de la Ligue final - a result that will have serious ramifications on the French title race.