The EFL and its members decided instead at a meeting on Thursday to press ahead with a plan to return the league to 72 clubs by relegating only one side from the fourth tier at the end of the current campaign.
An EFL statement said: “During today’s meeting, the EFL and its member clubs considered and debated a number of options, with all clubs given the opportunity to air their views.
“The debate included consideration of the proposal submitted by the Bury FC Rescue Board for the club to be admitted to League Two under new ownership in season 2020-21.
“Following in-depth discussions, it became clear that the proposal did not have the necessary support and that EFL clubs favoured extending the existing principle of a reduction in relegation across all divisions as a means of returning to 72 clubs now and for the future.”
Bury were expelled from League One and the EFL in August after the collapse of a proposed takeover following the postponement of their first five fixtures after the Shakers were unable to provide proof of their ability to fund the season.
The Rescue Board, chaired by Bury North MP James Frith, had appealed to EFL members to support its readmission, but their plea fell on deaf ears.
EFL executive chair Debbie Jevans said: “While we are saddened that Bury are no longer part of the EFL, the board’s difficult decision to withdraw membership was only taken after every opportunity to find a resolution was exhausted.
“Since then, in recognition of the efforts made on behalf of the club, the EFL has engaged with supporters’ groups, shared their submissions with our members and debated at length the issues raised.
“Following the discussion today, clubs have established that the preferred direction of travel is to reduce relegation from League Two as a means of returning to 72 clubs. The clubs felt that, in a difficult situation, this approach maintains fairness for all members and upholds the principle of the football pyramid.”
Meanwhile, the clubs have backed the proposed appointment of former Liverpool and Premier League chief executive Rick Parry as the new EFL chairman.