Brewster alleged Mironov had racially abused him during a UEFA Youth League clash in December, reporting the defender to referee Mohammed Al-Hakim at Prenton Park.
The following day UEFA launched an investigation into the case in which an inspector took statements from five players from both teams and the match officials.
None of the players interviewed heard any discriminatory words, UEFA confirmed on Wednesday, while Mironov admitted he swore at Brewster but insisted there was no racist element to his outburst.
With the UEFA-appointed Ethics and Disciplinary inspector finding "no evidence to corroborate the allegations", Europe's governing body has opted not to sanction Mironov.
In confirming the decision, UEFA said: "Following the opening of proceedings, UEFA appointed an Ethics and Disciplinary Inspector to conduct a thorough independent investigation and gather potential evidence relating to the case. Such an appointment is standard practice, given that allegations of racist behaviour are taken very seriously by UEFA and its disciplinary bodies in accordance with our zero tolerance policy towards any kind of discrimination.
"The inspector took statements from five players from both teams, as well as from two match officials, who were in the vicinity of the alleged incident. None of these heard any discriminatory words.
"Leonid Mironov was also interviewed by the inspector and stated that he indeed swore at Rhian Brewster, but he unreservedly denied using any discriminatory language.
"After concluding his investigation, the inspector found no evidence to corroborate the allegations, which he believed were made in complete good faith by the Liverpool player Rhian Brewster.
"Therefore, the UEFA Control, Ethics and Disciplinary Body, following the recommendation of the inspector, established that there was no evidence that would legally support sanctioning the FC Spartak Moskva youth player Leonid Mironov and thus decided to close the disciplinary proceedings.
After the incident Brewster accused UEFA of brushing racism "under the carpet" in an interview with The Guardian, leading to the Football Association to complain to UEFA and FIFA that such incidents were not being taken seriously.
Speaking in December, Brewster said: "Everyone stands behind the anti-racism banners. You have the adverts for Champions League games saying 'no to racism' in all the different languages. Idols of the game take part – but it still happens.
"I'm thinking to myself: 'Well, I'm standing behind a banner but does it really stop them from saying it?'
"To be honest, I don't think there is any point. It needs more severe punishments. I don't think UEFA take this thing seriously.
"They don't really care. That is how it feels anyway, like it has been brushed under the carpet."