In a dramatic move, cricket's world governing body announced Friday that Speed was to go on paid leave for the final two months of his contract following a "fundamental breakdown" between himself and several board members, including the current ICC president, South Africa's Ray Mali, over the controversial issue of Zimbabwe.
"That has not been imposed on him (Speed), it is something I have done with the president and chief executive," Morgan told a news conference at Lord's here Saturday.
Morgan confirmed the extraordinary development was prompted by Speed's unhappiness at the way in which the ICC dealt with Zimbabwe.
The 59-year-old Speed was particularly frustrated by the ICC board's failure, following its March meeting, to take any significant action against Zimbabwe Cricket (ZC) after an independent forensic audit carried out by leading accountants KPMG raised questions about the state of ZC's finances.
"Zimbabwe is an issue where the president and the chief executive have disagreed, there is no doubt about that," said Morgan, previously chairman of the England and Wales Cricket Board.
"You know what the board decision was in relation to the KPMG report, Mr Speed was clearly uncomfortable with that."
Defending the ICC's decision not to publish the KPMG report, Morgan added: "The thinking behind that reflected the extremely difficult trading position that exists in Zimbabwe.
"It was very clear the report identified no particular individuals who were guilty of any financial mismanagement or malpractice. It was against that background the board decided the report shouldn't be made public."
Now, for the first time in its 99 year-history, the ICC's annual conference is set to move away from Lord's and instead be held at the organisation's Dubai headquarters in July.
That move has been prompted by doubts over whether Peter Chingoka, the ZC chairman, would be admitted to Britain.
"He applied to the British authorities in Harare to attend this year's annual conference," Morgan explained.
"That visa has neither been granted or refused. The ICC at its last board meeting took a decision that if it wasn't certain that Mr Chingoka was going to be in possession of a visa by April 15 then the conference week would be relocated from here to Dubai."
England's hosting of next year's ICC World Twenty20 has been threatened by the British government's hardline opposition to the regime of Zimbabwe president Robert Mugabe and his ZANU-PF party.
However, Morgan said: "The ICC World Twenty20, in my opinion, will go ahead at the two grounds in London (Lord's and The Oval) and at Trent Bridge. I'd be very surprised if that didn't happen."
Speed's exit has again raised questions as to whether ICC can rise above the self-interest of its members and run world cricket effectively.
Morgan, whilst insisting a "huge amount" had been achieved during Speed's seven years in charge, admitted the ICC's image was "not good".
He added: "I do not believe at all times we govern in the optimum way but govern we certainly do."
David Richardson, the ICC's general manager, will serve as interim chief executive until the former South Africa wicketkeeper's compatriot Haroon Lorgat takes over as planned as chief executive in July.