German referee Felix Brych twice halted the Group G match for several minutes - first late in the first half and again shortly after the interval - after home fans lit flares and the pitch became enveloped with heavy smoke.
On Thursday Zenit issued a harshly-worded statement to explain the situation.
"Zenit consider unacceptable a situation when actions of some individual supporters have a negative effect on the course of a game and could lead to heavy disciplinary sanctions including a forfeit," the Russian champions said on their website.
Zenit said, following an agreement between the club and police, searches on fans entering the stadium were less thorough than usual because of cold weather.
"In the next few days the club and police, with the help of UEFA and the Russian FA, will conduct an investigation and will issue much tougher rules in regards to searches of fans before entering the stadium," the club added.
European football's governing body said they would make a decision on the incident in the next few days.
"We're in a process of collecting information in relation to the events at the game and when we have all the facts we will make a decision," a UEFA spokesman said.
Zenit midfielder Roman Shirokov called the home fans "real idiots" after they ignored his pleas to stop their fireworks.
"They are real idiots, what else can you say?" the outspoken Russia international told reporters. Zenit goalkeeper Vyacheslav Malafeyev said the incident had disrupted the his team's flow and had cost them victory.
APOEL held Zenit to a 0-0 draw to become the first team from Cyprus to reach the knockout round of Europe's premier club competition.
Zenit are second in the group and will guarantee progress to the last 16 if they draw with or beat Porto in their final group game in Portugal next month.
