In an interview with The Guardian, Brewster accused UEFA of not taking racism "seriously" and said it felt like occasions when he was on the receiving end of abuse during UEFA Youth League matches had been "brushed under the carpet" by European football's governing body.
The 17-year-old striker recounted several instances of racial slurs, including one from an opposition player during England's Under-17 World Cup final win over Spain in October – a tournament Brewster finished as top scorer.
In a statement, the FA outlined difficulties encountered when trying to report incidents as a particular concern.
The statement read: "We take such matters extremely seriously and have worked to provide support to our young players should they be the victims of such abhorrent behaviour while representing club or country.
"In Rhian’s case, we have visited him at his club to discuss his concerns and understand his frustration at the perceived lack of action. He has our full support and we will continue to push for appropriate responses from the relevant authorities.
"We have raised with both UEFA and FIFA a need for discrimination to be covered as part of the pre-tournament player workshops, and also expressed our concern at difficulties encountered in trying to report incidents.
"Our hope is to work closely with UEFA and FIFA to learn from these issues and to ensure a better way forward in order to protect young players."
At the start of December, Liverpool lodged an official complaint to UEFA after Spartak Moscow defender Leonid Mironov was purported to have made a racist comment towards Brewster. That led to a charge and a hearing likely to take place early next month. UEFA's disciplinary regulations stipulate that any player found guilty of racist abuse should be banned for a minimum of 10 matches.
In Liverpool's previous meeting with Spartak in the competition, supporters of the Russian club directed monkey chants at black players and the subsequent punishment was a fine, the closing of 500 seats in their academy stadium and being forced to display an "Equal Game" banner in that area of the stand.
"It's not really a punishment, is it?" Brewster said in his Guardian interview. "It was nothing really, a slap on the wrist. They weren't even using those seats.
"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."
Liverpool manager Jurgen Klopp underlined at a news conference on Friday that Brewster has the club's full backing.
"He will get all the support he needs and wants and that we can give," Klopp said.
"I'm really long in this business, in this sport, and I've never faced a situation like that. That means then, to a lot of people, actually you think it doesn't happen, but obviously it happens all the time.
"I'm really happy that he is brave enough - and you need to be brave - to do what he did. It's such an important thing .
"I really can't believe people have these kind of thoughts still in their minds. It’s so strange in this world that it happens. We needed a 17-year-old boy to show that it still happens and that it’s happening all the time. We need to stop it."