World football governing body FIFA fined the Russian football federation 30,000 Swiss francs (25,000 euros) after Manchester United midfielder Pogba and Barcelona winger Dembele were the target of monkey chants during the 3-1 French victory in March.
"Seven people have been identified for these incidents. They should be punished," said Sorokin, the chief of the Russia 2018 organising committee, at a World Cup presentation in a Parisian hotel.
Sorokin said the punishments would be "five match bans or maybe, if the offences were serious enough, life bans".
"Racist incidents can happen and we are no exceptions in Russia," Sorokin said. "In recent years, we have seen that the number of such incidents fall in international and first division matches.
"They are rare. We are truly sorry that it happened during the friendly against France."
He said Russian football authorities "are working hard to prevent such incidents, and to explain to fans that this kind of behaviour is not acceptable".
He added that each World Cup stadium would have 1,200 cameras "to identify anyone who might do something like that".
New FIFA rules also meant "referees could suspend matches in such cases", Sorokin said.