Consecutive defeats to Norwich City and Schalke 04 have led to fans becoming disgruntled at the club's direction, but Gazidis has urged patience among supporters.
"In the next two years, we will have the financial resources to sit and compete among the leading clubs in the world, which is an extraordinary achievement," Sky Sports News quotes Gazidis as saying.
"Financial success is relevant because it supports our football vision... the money we make is made available to our manager and he decides how to invest those funds.
"Arsene has done a magnificent job against the spending of our major competitors."
Arsenal are currently ninth in the Premier League with 12 points from eight games.