England won the game 6-0, but the first half was marred by abuse directed at Tyrone Mings and Raheem Sterling in particular, whenever they touched the ball.
Monkey chants could be heard in the stadium in Sofia and some fans even made the Nazi salute during play.
In response to UEFA's sanctions, the president of football's governing body demanded "new, stronger and more effective ways to eradicate racism in football", calling for worldwide life bans for those found guilty of racist behaviour.
“So many times we say there is no place for racism in football, but nonetheless we still face challenges to tackle this problem in our sport, as we do in society," said FIFA President Gianni Infantino.
“I call on all football governing bodies to join us and think together of new, stronger and more effective ways to eradicate racism in football.
"As a starting point, I suggest that all competition organizers enact regulations which envisage life bans from stadiums for those who are found guilty of racist behaviour at a football match.
"FIFA can then enforce such bans at a worldwide level.”
UEFA's boss earlier blamed a rise in nationalism for fuelling racism at football matches and said the European governing body was committed to eradicating the "disease" of racism from football and imposing strong punishments.
Aleksander Ceferin said was defiant about UEFA's stance on erasing racism, saying: “As a governing body, I know we are not going to win any popularity contests, but some of the views expressed about UEFA’s approach to fighting racism have been a long way off the mark.
“Football associations themselves cannot solve this problem.
“Governments too need to do more in this area.
"Only by working together in the name of decency and honor will we make progress."
Earlier on Tuesday, the head of the Bulgarian Football Association, Borislav Mihaylov, resigned from his position.
The former goalkeeper stepped down after the country's prime minister Boyko Borissov urged him to quit after Monday's match.
Mr Mihaylov wrote to UEFA before Monday night's match criticising the fact that England players had spoken about the potential for racist abuse during the fixture, calling it an "unjust branding" of Bulgarian supporters and urging UEFA to impose sanctions if England did not follow protocol.
Former England defender Joleon Lescott told ITV News that stronger sanctions need to be in place.
"No one is doing enough, i think there needs to be an extreme action taken so even the bodies and the actual individuals fear the consequences," he said.
"If all they're getting is a slap on the wrist then [it will happen again] unless they're getting proper consequences where it can affect their livelihood."
The ex-player said he did not "think the people making the decisions" about sanctions "are of colour".
"I think the people in the board that are sitting around the table and saying 'yeah this is what needs to happen' haven't experienced it enough to know how angry you get from those remarks."
He added that homophobic remarks should offend people who are not gay and therefore black players are not the only people who should be angered by racism.
"This is not directed at Raheem Sterling or Tyrone Mings, this is all of us," he added.
Football fan, Adi Fadare-Chard, who was in the stadium told ITV News that players should consider leaving the pitch after racist incidents, something he said would be a "brilliant" way "to make a stand".
He added: "I feel it would really highlight it across Europe, but then at the same time, does that mean that the racists win?"
He said the stoppages highlighted the problem and was pleased they stayed playing, as "the football did the talking."
Prime Minister Boris Johnson has condemned the racism at England's match as "vile" and called on UEFA to conduct a swift investigation with tough penalties to follow, Downing Street said.
"The racism we saw and heard last night was vile and has no place in football or anywhere else," the official spokesperson said.
"The England players and management showed tremendous dignity and the Prime Minister commends the players who were targeted with this despicable abuse for their response."
England boss Gareth Southgate said he is proud of the way his players handled the "abhorrent" racist abuse, but said his players were "hardened to racism" because of their experiences in the UK.
He added: "They are in the dressing room smiling because they've played so well.
"They also know they've made a statement and they want the focus to be on the football.
"We will recognise there's been an opportunity tonight to raise awareness of this issue. I think that has happened."
England captain Harry Kane called for "stronger punishments" for racism following the match's two stoppages.
"It is unacceptable to be racist once so I feel there can be stronger punishments and protocols but from our point of view as a team, we stuck together, showed unity and did what we had to and that is the most important thing," the captain said.
He added: "There's no room for racism in football or society."
But Bulgaria coach Krasimir Balakov claimed not to have heard anything amiss during the match.
"I did not hear the chanting...I saw that the referee stopped the game, but I also have to say the unacceptable behaviour was not only on behalf of the Bulgarian fans but also the English fans," Balakov said.
He added: "For three weeks all we've heard people talking about is anything else but football."
UEFA also charged the Bulgarian Football Union with the "throwing of object", disrupting the national anthem, and issues involving screen replays.
The FA was also charged with disruption of the national anthem and for failing to provide enough travelling stewards.
This was England's second Euro 2020 qualifying match marred by racism as players were racially abused in Montenegro.