The move follows a row surrounding Mr Ashcroft, whose main business interests are in Belize and who has been a major donor to the party in recent years.
He is suing The Times over allegations the newspaper made about his business dealings in Belize.
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Mr Stafford told BBC Radio 4's Today programme that this motion was "another step in the direction of making the party much more democratic".
But after losing the vote he said party officials had told him his motion was "untimely" and risked embarrassing the party.
Speaking earlier, Mr Strafford had said: "There's been a huge amount of press coverage of the transfer of assets et cetera and people had thought the Conservative Party had moved away from that.
"My case is that the members should have the right to choose who the treasurer is."
Last week, Mr Ashcroft was praised by the Tory chairman Michael Ancram, for increasing the number of donors giving money to the party, among which was Mr Ashcroft himself.
But Mr Strafford said shadow cabinet ministers had admitted privately to him they agreed with his campaign, although they would not support him publicly.
He said: "They try to keep these things quiet and they don't want any form of dissent from the rest of the [shadow] cabinet"
Mr Stafford said: "I'm quite certain within the next six months the party will decided to have an elected treasurer, even if it doesn't today."
A-Z of Parliament
Talking Politics
Vote 2001
Increase in Tory donors
(29 Sep 99 | UK Politics)
Ashcroft sues over allegations
(21 Jul 99 | UK Politics)
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