"I recognise that an important part of the role is liaison with FIFA, our global governing body. I am not prepared to deal with people whom I cannot trust and I have withdrawn my candidacy," he said in a statement.
He added that England's bid team in Zurich, which included Prime Minister David Cameron and the second in line to the throne, Prince William, were promised votes which had not been delivered by the Executive Committee (Exco) members.
Burden, who was appointed in May after rising through the ranks of the FA as representative for Gloucestershire in central England, said he would continue as acting chairman until a successor could be found.
His decision followed a day of recriminations over England's bid, which attracted just two votes out of 22 - one by their own representative - from FIFA's executive committee in Thursday's poll to decide the venue for the 2018 World Cup.
The decision went to Russia which will stage soccer's biggest showpiece for the first time. Qatar beat the United States and three others in the vote to decide the hosts in 2022.
"I have no issue with Russia's winning bid. I am sure they will put on a great World Cup and I have congratulated them," Burden said.
WIDELY ACCLAIMED
"We were equal top of FIFA's own technical assessment of the four bids. We were top of an independent assessment of the best commercial bids and our presentation on Thursday was widely acclaimed as the best of the 2018 and 2022 bids.
"Against this background, I am struggling to understand how we only achieved two votes. It is difficult to believe that the voting was an objective process.
"On top of that, Prince William, the Prime Minister and other members of our delegation were promised votes that did not materialise."
Burden, who succeeded David Triesman who himself stood down after making leaked allegations of a corrupt 2010 World Cup plot between Spain and Russia, declined to blame the British media for England's failure in the vote at FIFA's Zurich HQ.
"I am well aware that some of the UK media coverage could have upset some of the FIFA executive committee. We have a free press in our country and we all have to live with adverse comment from time to time."
Earlier on Friday, England's bid chief Andy Anson suggested FIFA President Sepp Blatter influenced Exco members before the vote by reminding them of British media stories which alleged corruption against them and led to two being banned.
He said that unless the selection process was changed it was not worth bids like England's bothering with the process.
"When you have the best technical bid, fantastic inspection visits and the best economic report - and from what people told us the best presentation yesterday - it's quite hard to stomach that seemed to count for absolutely nothing.
"Having only 22 guys voting gives them too much power and influence."
