Russia's victory in the 2018 race was followed by the huge surprise of Qatar beating the United States in the fourth round of voting to win the right to host the 2022 event.
"If you look at the technical process, the people who got the best reviews went out earliest, while the people who get the toughest reviews seem to have won," said Anson.
"The technical report is £3m down the drain by the looks of it. We spent £3m on it and it was the best one. The two bids with the worst technical reports won."
He also expressed bitterness at the way the vote had turned out to be tactical.
"There were other votes we thought we were going to get that would have taken us way into the second round and beyond," he added.
"Some of those didn't materialise, I don't know which ones.
"When people look you in the eye and promise you something, you hope they live up to their word, but clearly that hasn't happened."
Prime Minister David Cameron, who was part of England's presentation team on the day, called the news "bitterly disappointing" and said it was hard to see what else could have been done.
Fifa should review voting 'framework' - Coe
"I think, according to Fifa we had the best technical bid. No-one could identify any risks of coming to England. I think we had the strongest commercial bid and the country is passionate about football. But it turns out that is not enough," he said.
"It is hard to see what more you can do, but in the end it turns out, having the best technical bid, commercial bid, the passion for football, that is not enough.
"It's desperately sad, there has not been a World Cup in my lifetime in England. I was hoping we could change that, but not this time."
England bid board member Lord Coe, who headed the successful London 2012 Olympic campaign, said he could not find fault with the bid and that Fifa needed to look at its voting procedure.
"Fifa will have to look at what they've presided over the last few weeks and month and decide if this is the way they want to continue in the bidding process," he said
"I think probably they're going to have to look at the framework.
"I'm only sorry that the bid team today weren't fully able to get the message across.
"I believe England was pre-eminently the best bid at the table. We will stage a fantastic Olympic Games in the same way we would have staged a fantastic World Cup."
Premier League chairman Richard Scudamore said the fact England have facilities already in place appeared to have counted against them.
"They have decided to take the World Cups to developing areas," he said. "What's gone against us is not having to build 20 new stadia. It almost feels as if we are on standby for when somebody can't host it.
"That's all very well - but on that basis we will never get it."
Former Football Association executive chairman David Davies said he was "desolate" at the news, and said the England bid team had been let down over promised votes.
Fifa is an organisation that doesn't have to answer to anyone. What did we expect?
Former England manager Graham Taylor
"Clearly, the reason the team feel so let down is that they genuinely accepted the promises that they had received were going to get support in what we all knew was going to be the difficulty of the first stage and certain people did not deliver. Why did they not deliver?" he said.
"I heard one particular European voter who all the way through had seemed to be a certainty for England, let England down at the last minute. Now that was extraordinary."
He also said the role of the English media may have scared some people off backing the bid.
"The problem with the English press as it was put to me was 'do we want to live with the English press for the next seven-and-a-half years?' which is a big question," he said.
"Some of us who've been in this rough and tumble world of the British media just accept it as that and don't complain too much.
"There is no question that there is a different view abroad."
Former FA chief executive Mark Palios also thought press coverage may have played a factor.
"I think that may well be a feature. To see why we actually came nowhere near and underneath the Belgium/Holland bid, it sounds like it's almost payback time," he said.
"I've never heard a compelling explanation of the timing and the public interest [of this week's BBC's Panorama investigation into Fifa corruption allegations].
"It may well have an impact - that and the natural disposition towards the British media. I don't think that would have helped at all.
What went wrong with England's 2018 bid?
"I think looking at the extent we did lose, there might be a deeper seated problem than just the Panorama problem."
England 2018 ambassador David Beckham added: "I've heard the rumours that we lost due to the British press. I hope that isn't the reason. I believe in a free press and they are incredibly supportive of the game I love."
Former England manager Graham Taylor also dismissed criticism of the media and said nothing about Fifa surprised him any more.
"I'm just surprised that we're surprised," he said. "Fifa is an organisation that doesn't have to answer to anyone. What did we expect?
"Fifa for me is full of people who say 'yes' to your face and 'no' behind your back. Their reputation has not changed over many years.
"England have had little or no influence. We are considered to be arrogant and know-alls."
He also defended the English media, whose investigations into Fifa have been cited by some people as one of the reasons for the bid's failure.
"I'm not one of those blaming Panorama or the Sunday Times - this has been going on for years," he said.
"I just have a feeling that perhaps, just perhaps, it might now be time... they really need looking into, they should really be investigated - and of course our journalists are very good at that."
Taylor also criticised the decision to give the 2022 World Cup to Qatar, adding on BBC Radio 4's PM programme: "It really is surprising. Where is the heart and soul of football in Qatar? And yet that decision has been made."
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