The RFU Disciplinary Committee said they found no evidence of racism after Frimpong claimed he was subjected to monkey chants at the first match of the Russian Premier League season last Friday.
The 23-year-old former Arsenal player was sent off after he raised a finger to the crowd in response and was suspended for two Premier League matches.
"We live in a crazy world," the Ghanaian wrote on Twitter.
"For the Russian FA to say they didn't hear or see any evidence of racism is beyond a joke."
The midfielder, who apologised for his reaction, was invited to attend the Disciplinary Committee hearing but did not appear.
"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," the head of the Disciplinary Committee Artur Grigoryants told reporters.
"There were no instances of racism. We have no grounds to take disciplinary sanctions against Spartak.
"Frimpong has been banned for two games for the offensive gesture he displayed towards the stands."
The Russian Premier League's security director Alexander Meytin also said the league had not found any evidence of Spartak Moscow fans racially abusing Frimpong.
"The video cameras did not pick up any evidence of gestures. There were no gestures aimed at the footballer," Meytin said in an interview with Russian sports website Championat.com.
"We asked the stewards. They did not see anything either from the fans," he added.
Football's world governing body FIFA had said it would ask the RFU to provide details of the incident.
(Reporting by Dmitriy Rogovitskiy; editing by Ken Ferris and Toby Davis)
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