The defeat left Zenit seventh in the 16-team Russian league with 24 points from 17 games, 10 points adrift of leaders Rubin Zazan.
Advocaat led Zenit to the Russian title in 2007 and their greatest success a year later as they won the UEFA Cup, beating Glasgow Rangers in the final.
But the success led to the departure of several high-profile players, including Andrei Arshavin to Arsenal in the English Premier League, and results have suffered.
Advocaat was due to end his contract at the end of the current Russian season to take over as coach of the Belgian national team, but club officials lost patience with him.
"Unfortunately, after the (Advocaat's) decision to take over the Belgium national team, Zenit's results have noticeably gone down," the club said in a statement on their official Web site www.fc-zenit.ru.
"Both fans and the management are dissatisfied with the place Zenit holds in the Russian championships," it added
Anatoly Davydov, the club's reserve team boss, was appointed interim coach and will be charged with lifting them up the league to challenge for a place in European club competition next season.
Advocaat has previously coached the national teams of the Netherlands, South Korea and the United Arab Emirates, as well as PSV Eindhoven and Scottish League champion Rangers.The Dutchman had been at Zenit since 2006.