The Easter Road side received fewer than 18,000 tickets for the showpiece fame against Celtic on December 19 – a decision that manager Jack Ross said he found baffling.
He added: “I can understand the reallocation of tickets, I can understand segregations issues, but I think Hampden is a stadium that can be segregated quite easily.
“I just can’t quite fathom it. I understand fans having bigger and smaller fan-bases and I understand there will be a ceiling on the numbers that clubs will sell.
“But when you have us involved in it, and our recent cup final involvement when we have sold big, big numbers, that there wouldn’t be the willingness to put that in place, I don’t quite get it. I don’t quite understand it.”
The Capital club has nevertheless announced details of the ticket sale for next month’s final, which starts on Friday November 26.
A club statement read: “We have received in the region of 17,500 tickets for the final at Hampden, with tickets sold on a first-come, first-served basis.
“We are extremely frustrated with the allocation we’ve been given and made our thoughts very clear to the SPFL.
“We are in constant discussions with them pushing and persuading them to give us additional tickets.”
Season ticket-holders will be able to buy a ticket for themself and one other individual from 2pm on Friday either online or over the phone.
Any remaining tickets will go on sale from 10am on Tuesday November 30.
A club spokesperson added: “We know the significance of these sale dates and how important it is that we make this fair for all our supporters.
“With that in mind, we wanted to reward all the Hibees that backed us in a terrific manner at Hampden in the semi-final. Unfortunately, we don’t have the data for the additional tickets purchased by season ticket holders and supporters.
“We felt it was vital to reward, and thank, our season ticket holders for their support, which is why they’ve been given first priority and can purchase an extra ticket.
"We’d like to thank you all for your magnificent support and will keep pushing for additional allocation.”