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Brewster, who won the Under-17 World Cup with England in October, was visibly irate at the end of Liverpool's 2-0 win over Spartak in the UEFA Youth League and had to be restrained by team-mates and coaching staff.
Following the incident at Prenton Park, home of Tranmere Rovers, Liverpool said only they had "followed the proper procedure by reporting the alleged incident to UEFA".
Their complaint is understood to concern a matter of racist abuse.
The matter arose shortly before the Champions League group game between Liverpool and Spartak's senior teams at Anfield.
Liverpool lodged a similar complaint against Spartak after Brewster's team-mate Bobby Adekanye was racially abused by the Russian club's fans during the reverse fixture in September.
Spartak were found guilty in that instance and were made to partially close their academy ground for one match.
