The Safety Advisory Group - chaired by Glasgow City Council - has, however, not ruled out the principle of installing rail seating at Celtic Park.
Its use has been pioneered at stadiums in Germany, and Borussia Dortmund's Westfalenstadion can accommodate 27,000 standing fans.
Celtic had hoped to become one of the first clubs in Britain to introduce a safe standing area, which would hold 2700 people.
There is concern that all-seater stadiums, introduced after the Heysel and Hillsborough disasters, are too constraining and rob the game of much of its atmosphere.
The rails incorporate seats that can be flipped up to allow standing. Bristol City has become the first UK club to install them.
A spokesman for the safety group, made up of agencies including police and the fire service, indicated the proposal could be reconsidered if issues including proper segregation and increased stewarding were addressed.
Joe O'Rourke from the Celtic Supporters Association attended a three-hour meeting with independent expert Dr Steve Frosdick, who backed Celtic's plan.
Mr O'Rourke said he could see no reason for the safety group to reject the proposal, and there were already plans for increased stewarding.
He said: "I am shocked by it, absolutely horrified, because Celtic could have led the way. If they were allowed to install it, it would have opened the floodgates after that. Lots of clubs across the whole of the UK would apply to do it."
The safety group spokesman said it was felt Cetic's stewarding plan for the standing area was insufficient to ensure spectator safety.
The group wanted physical separation, such as a barrier, between standing and seating areas.
Celtic FC said it was "extremely disappointed" with the decision, saying it had made "every effort to address comprehensively" issues raised.