The result extended Montpellier's winless run to eight matches in all competitions, leaving them fourth from bottom in Ligue 1 and five points clear of the relegation zone.
Speaking on Thursday, Fernandez said: "In the interest of the club and the team I have decided to quit."
Fernandez had only been in the role since the beginning of the season having taken over from Lille-bound former coach Rene Girard.
Deputy chairman Laurent Nicollin has revealed asssistant Pascal Baills will assume caretaker charge while the search for a new boss gets under way.
"We must quickly restore the joy and pleasure to the people who support us," said Nicollin.
Montpellier travel to Toulouse in the league on Sunday.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.