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.
Bizarre Jose Mourinho statement aims to pre-empt punishment after Fenerbahce boss clashes with Galatasaray counterpart
'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
