The Gunners took some 49,000 supporters to the national stadium for Saturday's semi-final against Wigan, which they won following a penalty shoot-out, after the Sky Bet Championship side returned some of their tickets.
However, the distribution by the Football Association for the final will see some 20,000 tickets distributed to volunteers through the 'football family', which includes counties, leagues, local clubs and charities, the 92 Premier League and Football League clubs, another 134 full member clubs and all those clubs who reached the third-round proper.
With the FA Cup final being part of the Club Wembley membership package, some 17,000 tickets will therefore also be allotted elsewhere.
Gazidis feels the system is unfair on both finalists and said on the Arsenal website: "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 show piece 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."
Arsenal plan to show the FA Cup final live at the Emirates Stadium, some 11 miles away from Wembley across north London, on giants screens for those supporters not able to attend in person.
"We want this to be a special day for Arsenal fans wherever they are, and the screening will be a great way for thousands of our supporters who are unable to get to Wembley to watch the match together at Emirates Stadium," Gazidis said.
The FA said allocations for the final have been around 25,000 per club ever since the new Wembley opened, and pointed out that ticket prices have remained the same for the last three years.
Apart from the 20,000 tickets that are distributed to volunteers and through the 'football family', a further 17,000 are taken up by the Club Wembley membership package where holders are guaranteed seats for the major events at the stadium.
- Sports & Recreation