"The club's shareholders made a decision that Unai Emery will no longer coach Spartak," Spartak director general Valery Karpin said after the match, adding that a decision on a new coach will be made in the next few days.
Emery was given a vote of confidence by Spartak owner Leonid Fedun just five days ago following a 3-0 loss to Barcelona in the Champions League, but after a second home thrashing in a week the axe finally fell on the Spaniard.
Emery was appointed Spartak coach in May, replacing former Russia international Karpin despite the team finishing last season in second place and qualifying for the Champions League.
The 41-year-old was given a two-year contract after he led Valencia to three consecutive podium places in Spain behind Barcelona and Real Madrid.
Spartak, Russia's most successful and popular club with nine league titles between 1992 and 2001, have not claimed any domestic trophies since winning the Russian Cup in 2003.
They started this season well but then fell into a slump after a spate of injuries to several leading players. They are in seventh place, 10 points behind leaders CSKA Moscow, who travel to St Petersburg to face champions Zenit on Monday.
Spartak have also failed to impress in Europe and have been consigned to finishing bottom of Group G with a game to spare.