Poyet, assistant manager Mauricio Taricco and coach Charlie Oatway were suspended by the Seagulls last month in the aftermath of the play-off semi-final defeat by Crystal Palace. Taricco has since had his suspension lifted but Poyet was due at a disciplinary hearing on Monday morning.
Brighton released a statement revealing the Uruguayan did not show up, but the LMA have countered that with a statement of their own showing support for Poyet.
It read: "Brighton & Hove Albion FC ordered Gus Poyet to attend a crucial disciplinary hearing today (Monday), despite the fact that he only returned from annual leave yesterday (Sunday) and the charges were not particularised until June 13.
"Further, the very lengthy appendices to the initial report comprise around 500 pages and these were also only delivered recently. Clearly Gus needs to have a fair and reasonable opportunity to respond to what we believe are unfounded charges against him.
"Also, it has repeatedly been made clear to the Club that Gus's LMA representative, Richard Bevan was not available to accompany him today, but was available to attend on Thursday 20 or Friday 21 June as well.
"These two dates fall within the five working day period for an employee to offer alternatives to the original date set by the Club as set-out in the Club's own handbook. We believe that our members are entitled to the same legal protections that other employees enjoy.
"Football clubs need to observe basic employment rights like any other employer in our view. Just to be clear, however, we are confident that Gus will demonstrate there is no case to answer in this matter.
"Notwithstanding these important points, the Club decided to go-ahead with the hearing in the absence of both Gus and Richard Bevan. Late this afternoon the Club agreed to adjourn and reconvene the disciplinary hearing to Thursday June 20 2013.
"The LMA is pleased that the Club has agreed to an arrangement whereby Gus and his chosen representative will be able to attend."