"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," UEFA said in a statement.
"Mironov was also interviewed by the inspector and stated that he indeed swore at Brewster, but he unreservedly denied using any discriminatory language."
UEFA said that the inspector believed England under-17 international Brewster's allegations were made in good faith before closing the disciplinary proceedings.
Liverpool acknowledged UEFA's findings and said they had accepted their decision.
"We would like to place on record our admiration for the courage shown by Rhian Brewster throughout this process and commend his exemplary conduct," a Liverpool spokesperson said.
"The club is very proud of the maturity, dignity and leadership Rhian has displayed in bringing focus to this issue and he will continue to receive our full support."
British anti-discriminatory body Kick It Out said in a statement that it was "deeply disappointed" with UEFA's findings, adding that their decision would only encourage those who wish to be abusive in the sport.
"Kick It Out believes there are issues with clubs, such as Spartak Moscow, who have been involved in several alleged racist incidents in recent years, receiving little or no discouragement by national and international football authorities in response to allegations of racism and discrimination," the statement said.
"This underlying issue is compounded with any action taken in relation to racist or discriminatory incidents rarely being appropriate. This current situation is intolerable."
In January, Spartak Moscow published a racially-charged tweet that sparked outrage in the international soccer community as Russia prepares to hold the World Cup this year.
In a video published on their account, the club showed three black players doing drills at a training camp in Dubai with the caption: "Look at how the chocolates are melting under the sun."
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Christian Radnedge and Toby Davis)
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