Brentford chief executive officer Jon Varney says there is "deep frustration" over the 10,000 capacity limit for the Sky Bet Championship play-off final.
More than 12,000 fans have now signed an online petition calling for the capacity to be increased for the EFL play-off finals, which begin with Brentford vs Swansea in the Championship decider on Saturday.
The two teams have both been critical of the decision to limit the stadium's overall capacity to 10,000, with only 4,000 tickets per side.
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They have called on the UK Government and football authorities to treat the play-offs similar to the FA Cup final, which welcomed more than 21,000 people as one of the Covid test events.
Varney told Sky Sports: "We're in constant communication with the EFL about increased allocation.
"I have every sympathy with the FA and the EFL they are pushing very hard but it definitely requires government intervention.
"There's just a sense of real deep frustration at the moment, not just for our fans, but for all the fans of the EFL play-off finalists.
"It is a real, real, ticketing challenge for everyone.
"In terms of Brentford alone, we've got 11,000 season ticket holders and we have an allocation of 4,000 so we will have a lot of unhappy fans at the end of this process."
Speaking about the FA Cup final, Varney added: "That's the part of the process we find nonsensical to be brutally honest.
"Just two weeks ago, Leicester, Chelsea, and [21,000] fans were in the stadium.
"Two weeks later and Covid is going in the right direction for the country and we are back down to 10,000.
"I think the other piece around that is the frustration that there were clearly advanced conversations going on between the Government, UEFA, and the FA about the Champions League final and there is no way I believe that was going to be limited to 10,000 fans.
"The fans of the finalist clubs have set up an online petition that is really gathering momentum. So we are hopeful but we are fast running out of time because the logistics of trying to get the tickets into the hands of fans is really, really challenging.
"I think we all saw on Saturday (during the play-off semi-final) that fans make football occasions. It was the first time we had a high volume of supporters in our new stadium for the play-off semi-final against Bournemouth and they were absolutely the 12th man and helped us overturn a two-goal deficit."