Macedonian referee Aleksandar Stavrev interrupted the match in Austria for a few minutes in the first half after a number of flares were thrown from the Zenit fans into the crowd below.
"Zenit strongly condemns the acts of hooliganism which nearly abandoned the Champions League match between our club and Austria Vienna," the Russian league leaders said in a statement on Thursday.
"Obviously, the troubles in the stands influenced our team's performance," Zenit said, adding the club will take actions to hand stadium bans on the hooligans.
Italian coach Luciano Spalletti described the trouble-makers as enemies and also said they should stay away from football grounds.
"The UEFA delegate said that the match can even be abandoned if the troubles continue," the 54-year-old coach told reporters. "It's not the first time we're in such situation due to fans' behaviour."
Last year, Zenit's league match against Dynamo Moscow was abandoned when the Dynamo goalkeeper was injured by firecrackers thrown by fans, leading to 3-0 loss for the St Petersburg team who were also forced to play two home games behind closed doors.
"Role of the fans is very important, they often give additional stimulus to overcome difficult situations in matches," said Spalletti.
"But if our fans come to vandalize, then it would be better if they don't come. We believe these people are our enemies and we don't want to see them in the stands."
The big spenders Zenit, owned by Russian energy giant Gazprom, created history when they became the first team to qualify for the Champions League knockout stages with only six points from six matches.
Spalletti's men went through thanks to Porto's 2-0 defeat at Group G table-toppers Atletico Madrid, who finished on 16 points.