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.
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