Pakistan set England 242 to win the game but the hosts lost their last five wickets for 17 runs and Butt responded to the ICC's decision to investigate his side by claiming there was a "conspiracy to defraud Pakistan and Pakistan cricket".
On Monday morning, Butt was reported to have told India's NDTV channel: "There is loud and clear talk in bookie circles that some English players were paid enormous amounts of money to lose. No wonder there was total collapse of the English side."
England's players were so shocked by the accusations levelled at them that they considered refusing to play the fourth one-day international against Pakistan at Lord's on Monday, which they went on to lose by 38 runs.
Captain Andrew Strauss "refuted the allegations" on behalf of the England team before the game and said he had "strong misgivings" about playing the last two matches of the five-match series.
However, Collier told BBC Sport: "We felt it was important that the game went ahead.
"We conveyed that as a board to the players and the players were absolutely fantastic and really got behind that decision.
We felt it was important that the game went ahead
ECB chief executive David Collier
"We've had a game and that was in the best interests of world cricket, England cricket, the ICC and the world game.
"We met with the players around midnight [on Sunday night] and talked to them about why the board was so concerned and why we had come to the decision that we did.
"It was a board decision. You have to say to them that it is a board decision and we have to take players on that journey. We have learned that from the past.
"We explained to them why we took the decision. That was the whole logic of the evening. It was difficult. There was a lot of soul searching."
Former ICC president Ehsan Mani has joined those criticising Butt's recent conduct and has called for the structure of Pakistan cricket to be revamped.
He told BBC Radio 5 live: "What Mr Butt said was totally uncalled for, unsubstantiated and he has done a lot of harm for relationships between England and Pakistan, and Pakistan and the ICC.
"Mr Butt needs to come up with evidence of proof to back up what he said.
"Pakistan cricket has very few friends and he is very good at losing them, as he has with England.
"I have been saying for a while that the whole government structure of Pakistan cricket needs some serious revamping."
Mani also defended the ICC's actions in suspending the three Pakistan players at the centre of the spot-fixing allegations.
"The ICC did what the PCB should have done and suspend the players straight away," he added.
"It doesn't matter whether they are guilty or not, that will come out in due course.
"For the good of the game the PCB should have taken the lead, they failed to do that and the ICC did the only thing they could do."
Meanwhile, former ECB chairman Lord MacLaurin told BBC Radio 5 live that England were right to consider legal action against Butt.
"I don't blame them for that," he said. "The ICC have got to look at all this malpractice in the game, and when you've got somebody like [Butt] sitting there then I worry about the future of cricket."
Minister for sport Hugh Robertson and Professional Cricketers' Association chief executive Angus Porter have backed the ECB's decision to finish the series which is tied at 2-2 with one game remaining, at Hampshire's Rose Bowl on Wednesday.
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