Chief executive Ivan Gazidis want the FA to increase the allocation of tickets given to both Arsenal and Hull City for next month's FA Cup final.
The Gunner and the Tigers have been handed just 25,000 for the Wembley showpiece on May 17.
Arsenal have 45,000 season ticket holders at the Emirates Stadium and some will be left disappointed because of the low number of tickets made available to the club.
Gazidis, who sits on Football Association committees, said in a statement:
"We are disappointed many of our supporters and also those of Hull City will be unable to get tickets to the cup final.
"We fully understand this is the showpiece FA fixture to celebrate the game as a whole, but we also believe the loyal supporters of the competing teams deserve a greater chance to see their team play in what is one of the biggest matches of the season.
"The balance in the FA’s allocation system is not right.
"Arsenal have approximately 45,000 season ticket holders and 150,000 members, many of whom come to games.
"They all give us their loyal support throughout a season but with the FA Cup final allocation at 25,000 there will be many disappointed Arsenal fans, who have supported the Club home and away for years, who will be unable to get a ticket to this historic match."It is unclear whether the club are fighting this decision with the FA. Last season both Manchester City and Wigan had their ticket allocations increased, with City receiving 31,000 and Wigan 25,000.