The Ufa player said he was the subject of monkey chants before being sent off for a gesture against Spartak Moscow.
Spartak will not be punished as the RFU said it found no evidence of racism.
"For the Russian FA to say they didn't hear or see any evidence of racism is beyond a joke," Frimpong tweeted.
"Been banned for two games - acceptable on my part for the gesture, no problems with that.
"I've always said we are blessed in England and how wonderful of a country it is. Not saying there isn't racism in England of course. Must stress not all Russians behave like that."
Artur Grigoryants, head of the disciplinary committee, said: "The match inspector and the match delegate did not note that there had been any disciplinary violations by Spartak supporters towards Frimpong in the match reports.
"There were no instances of racism. We have no grounds to take disciplinary sanctions against Spartak."
Ghana midfielder Frimpong, 23, apologised for his reaction but did not attend the hearing.
Last season, Dynamo Moscow's Congolese defender Christopher Samba was given the same ban for an identical offence.
Zenit St Petersburg's Brazilian striker Hulk has recently said racism happens at "almost every game" in the Russian league and that it is a genuine threat to the 2018 World Cup, which will he held in the country.
He said he had repeatedly faced monkey chants and also accused a referee of racially abusing him.
It was announced on Wednesday that the striker will be one of the star names taking part in the preliminary draw for the World Cup, along with compatriot Ronaldo, former Italy captain Fabio Cannavaro and ex-Cameroon striker Samuel Eto'o.
Former Arsenal midfielder Emmanuel Frimpong called the Russian Football Union 'beyond a joke' after he was handed a two-game ban for reacting to alleged racist abuse.