Usmanov is the Gunners' second biggest shareholder, just behind American sports mogul Stan Kroenke.
The Russian billionaire thinks that Arsenal's board are failing to provide manager Arsene Wenger with adequate support as he looks to win the club's first trophy since 2005.
Usmanov told Forbes Magazine: "We do not consider just qualifying for the Champions League to be the chief ambition of the club, and with all our hearts we support the team and wish them well for the new season.
"Victory is absolutely not ruled out, but the current politics of the club's management will leave Arsene Wenger and his team with fewer and fewer opportunities in the long run."
He also said that he has no plans to sell his stake in the North London giants despite being denied any involvement in the running of the club.
"I am a fan and I am not going to sell these shares at any time, since this is the club that I consider the best in the world," he added.
Arsenal being their quest for silverware in 2012-13 against Sunderland on Saturday, August 18.