Arsenal had taken 49,000 supporters to their semi-final on Saturday.
However, the FA are to offer 20,000 final tickets to volunteers and member clubs through the "football family". With the final being part of the Club Wembley membership package, some 17,000 tickets will also be allotted elsewhere.
Gazidis feels the system is unfair on fans both teams involved in the final. "We are disappointed many of our supporters and also those of Hull City will be unable to get tickets to the cup final. The balance in the FA's allocation system is not right."