Arsene Wenger's men will play Hull City in the final of football's oldest knockout competition at Wembley on May 17 after defeating Championship outfit Wigan Athletic on penalties in Saturday's semi-final clash at the national stadium.
Arsenal were allocated 49,000 tickets for that fixture but will receive just 25,000 for the final.
And Gazidis has taken issue with that, claiming it is unfair on supporters who will be unable to get a ticket for the showpiece.
"We are disappointed many of our supporters and also those of Hull City will be unable to get tickets to the cup final," he told Arsenal's official website.
"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."
When contacted by Perform, the FA stated that approximately 20,000 tickets will go to volunteers at county level and local football clubs, while a further 17,000 are allocated for the 'Club Wembley' membership package.
