Spartak supporters were accused of aiming monkey chants at FC Tosno and Cape Verde midfielder Nuno Rocha during a cup game, resulting in a partial stadium ban for the Moscow club and a £1,150 fine.
Zenit supporters, meanwhile, allegedly chanted Nazi slogans during a league game against Anzhi Makhachkala on April 14, leading to a £1,150 fine for the Saint Petersburg outfit.
Alexey Smertin, Russian football's anti-racism inspector, has claimed that his country is being unfairly singled out.
"I cannot say that [racist incidents] happen more often in Russia than in other countries," the former Chelsea player told the RIA Novosti news agency.
"We cannot fail to take the political situation into account. There is certain bias [against Russia] in this respect."
Russia will host the World Cup this summer, the tournament taking place between June 14 and July 15.