Fautrel and his assistants failed to notice that Monaco forward Dimitar Berbatov was in an offside position when he scored one and set up the other two goals for the visitors.
"I made judgement errors that changed the context of the game," Fautrel was quoted as saying by sports daily L'Equipe on Monday.
"There were two lads (the assistant referees) who were feeling very bad in the dressing room and a stunned refereeing team."
Lyon coach Remi Garde opted against criticising the officials.
"I am not going to talk about it because I would risk a suspension," he said.
The win put second-placed Monaco on 62 points from 29 games, eight behind Paris St Germain, who beat St Etienne 2-0 on Sunday.
Lyon are fifth on 45 points, eight adrift of third-placed Lille, who occupy the Champions League third round qualifying spot.
- Sports & Recreation
- Dimitar Berbatov