The Scottish champions have been investigating the possibility of becoming the first club in Britain to install designated safe standing areas.
The club were hoping SAG would support their plans to progress but, after talks between the two parties, the advisory body has requested additional time and supplementary information before finalising their verdict.
Peter Lawwell, Celtic's chief executive, is a confirmed advocate of the safe standing model as used in the Bundesliga and, although a Celtic statement made their dissatisfaction clear, the club have pledged to meet SAG's demands in a bid to win its backing.
"Celtic Football Club is disappointed and frustrated that approval could not be given at today's meeting of the SAG to grant permission to install rail seating in Celtic Park, designed to allow safe standing by supporters," read the statement.
"The club has provided detailed information in support of this proposal over the past two years and has made every effort to address comprehensively all issues raised by the SAG.
"The SAG has asked for further time and information to be provided before a final decision can be made.
"The club of course will provide the additional information requested and we will undertake to do this as quickly as possible. We will then seek an early meeting of the SAG to consider progressing this matter without further delay.
"This is an important spectator safety issue. It is also an opportunity for Glasgow and for Scottish football to lead the UK in this area and it is one which Celtic will continue to pursue.
"We look forward to the next meeting taking place and hope this matter can be resolved as soon as possible."