The 17-year-old - who is yet to make his debut for Liverpool's first team - claimed Thursday UEFA "don't really care" about racism.
The incident prompted Brewster to speak out in a newspaper interview, where he claimed that racial abuse had been a regular occurrence for him since aged 12.
The FA added they wanted to collaborate closely with UEFA and world governing body Federation Internationale de Football Association over the issue.
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Kick It Out, a football anti-racism organisation, praised Brewster, who also said an England Under-17 team-mate Morgan Gibbs-White was called a "monkey" by a Spanish opponent during the World Cup final, for going public. UEFA's disciplinary regulations stipulate that any player found guilty of racist abuse should be banned for a minimum of 10 matches.
"I'm thinking to myself: 'Well, I'm standing behind a banner but does it really stop them from saying it?'"
And Brewster believes complaints need to be dealt with better by the authorities - particularly UEFA, who failed to take action on several occasions when the striker was representing England and Liverpool.
"To be honest, I don't think there is any point". They don't really care.
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"I am really long in the business, in the sport, and I never faced a situation like that".
"That means to a lot of people then it doesn't happen but obviously it happens all the time".
"I am really happy he is fearless enough to do what he did because it is such an important thing", Klopp said.
"I can't believe that people have these kind of thoughts still in their mind, it's so odd in this world that is happens".
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"It's so unusual that it happens in this world now, and we need a 17-year-old boy to shout out and say it is still happening all the time and that we need help to stop it".