Their game was halted twice during the first half due to the abuse but England players decided to complete the match instead of walking off.
Sofia: Bulgaria's coach quit Friday over the 6-0 loss to England in a Euro 2020 qualifier which was overshadowed by racist abuse that sparked a storm of protest.
Monkey chants and apparent Nazi salutes during Monday's match in Sofia caused indignation in the football world and led to the resignation of Bulgaria's football federation chief.
Bulgaria coach Krasimir Balakov, who took over the team in May, said he handed in his resignation during a meeting of the Bulgarian Football Union (BFU) executive committee.
"I said that if I am the problem of Bulgarian football, I am handing in my resignation. There is no way back," the former midfielder told reporters after the meeting.
"I will keep my fingers crossed for the next manager as the situation is not rosy at all... The racist incidents during the game with England were the final straw."
Bulgaria are winless in seven Euro 2020 qualifiers -- losing four and drawing three -- and occupy the last place in their group.
They conclude their qualifying campaign at home to the Czech Republic on November 17.
Monday's game was halted twice during the first half due to the abuse but England players decided to complete the match instead of walking off the pitch.
The 53-year-old Balakov, a former national team star, apologised on Tuesday to the England players over the incidents.
On the eve of the match, Balakov had claimed that there was a bigger problem with racism in English football than in his country.
Five more Bulgarian football fans were detained Friday for taking part in the racist abuse, while police continued to look for five others, the interior ministry said.
Police have now identified 16 people suspected of being involved in the "abusive actions", it said.
A Bulgarian teenager was indicted Wednesday for "grave hooliganism", risking a jail sentence of up to five years, while five others, including one who is underage, were handed fines and bans from sports events.
British Prime Minister Boris Johnson and his Bulgarian counterpart Boyko Borisov alike condemned the incident.
Under pressure from Borisov, BFU chief Borislav Mihaylov tendered his resignation on Tuesday.
Bulgaria have failed to qualify for any major tournament since Mihaylov took charge of the BFU in 2005.
UEFA has opened disciplinary procedures against both Bulgaria and England for their fans' behaviour during the game.
FIFA president Gianni Infantino also pressed Thursday for a worldwide ban on spectators who abuse black footballers.
A total of 48 football fans have been subjected to one or two-year bans from attending sports events in Bulgaria and abroad, fines and community work since the beginning of this year, the EU member's police statistics show.