Ceferin blamed a rise in nationalism across Europe for fuelling racism at matches and said the governing body was committed to eradicating the "disease" from football.
"Believe me, UEFA is committed to doing everything it can to eliminate this disease from football," said Ceferin in a statement.
"We cannot afford to be content with this, we must always strive to strengthen our resolve.
"More broadly, the football family - everyone from administrators to players, coaches and fans - needs to work with governments and NGOs (non-governmental organisations) to wage war on the racists and to marginalise their abhorrent views to the fringes of society.
"Football associations themselves cannot solve this problem. Governments too need to do more in this area."
Slovenian Ceferin said football had become complacent in tackling racism.
"There were times, not long ago, when the football family thought that the scourge of racism was a distant memory," he said.
"The last couple of years have taught us that such thinking was, at best, complacent.
"The rise of nationalism across the continent has fuelled some unacceptable behaviour and some have taken it upon themselves to think that a football crowd is the right place to give voice to their appalling views."
Meanwhile, president Borislav Mihaylov has resigned in the wake of racist abuse directed at England players, the Bulgarian Football Union has announced.
Mihaylov had been under pressure following Monday's events, and was reportedly urged to stand down by Bulgarian prime minister Boyko Borissov on Tuesday morning.
UEFA has now opened disciplinary proceedings against both Bulgaria and England.
Charges against the Bulgarian Football Union (BFU) include the racist behaviour, throwing of objects and disruption of a national anthem by home supporters, and showing replays on a giant screen.
The English Football Association has also been charged with disruption of a national anthem, as well as providing an insufficient number of travelling stewards.
According to a UEFA statement, the case will be dealt with by the governing body's control, ethics and disciplinary body, with the date of the meeting yet to be confirmed.
An FA spokesperson told the PA news agency: "We acknowledge the charges but will not be commenting further as it is an ongoing process."
Sports minister Nigel Adams has written to Ceferin on behalf of the government.
"The terrible events last night demonstrate clearly that much more needs to be done to stamp racism out of the game, once and for all," he wrote.
"I urge UEFA to take urgent action to ensure that all football authorities and fans are clear that the consequences of failing to tackle this issue will be severe.
"The England team has my full support and I welcome tough action from UEFA in response."
Adams, who also addressed the issue in Parliament, praised the conduct of England's players and management in Sofia.
"As I am sure you will agree, no player, manager, supporter, or participant in sport should have to tolerate discrimination of any kind," he added.
"The England players and management showed tremendous dignity and I am incredibly proud with how they conducted themselves throughout the match.
"It was a step in the right direction to see the UEFA protocol engaged during the match, but there is much more that needs to be done.
"I appreciate that is it for the English FA to work directly with UEFA on this important issue, including what action will be taken next following the events of last night."
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