Play was stopped twice in the first half due to monkey chanting by Bulgarian supporters with announcements made to fans that the game could be suspended if offensive chanting continued.
"We can confirm that England players were subjected to abhorrent racist chanting while playing in the Euro 2020 qualifier against Bulgaria," the FA said in a statement.
"This is unacceptable at any level of the game and our immediate focus is supporting the players and staff involved.
"As we are sadly aware, this is not the first time our players have been subjected to this level of abuse and there is no place for this kind of behaviour in society, let alone in football.
"We will be asking UEFA to investigate as a matter of urgency."
England players were also the target of racism during a 5-1 win in Montenegro in March.
A section of 5,000 seats at the Vasil Levski National Stadium in Sofia was already closed for the game after racism during games against Kosovo and the Czech Republic in June.