Wenger's comments come after Arsenal were criticised by Uzbek billionaire Alisher Usmanov, the club's second-largest shareholder, for withholding funds from the manager.
Usmanov - whose Red & White Holdings group are not represented on the board - also hit out at the Gunners board for their decision to sell Robin van Persie to Manchester United.
"This decision was a mistake," Usmanov said. "If I am one of Wenger's players I would want to stay for the finish, but he explained Robin wanted to go to win trophies."
But Wenger is adamant he has supported the decisions from the boardroom as he believes they have put the club's best interests first.
"I believe I have always had the support from the board, and am very grateful for that," Wenger said.
"We have worked over the years in respecting in what we did, which is to always work within our financial resources.
"Therefore we made decisions which from outside looked not based on purely footballing reasons, but it was based as well on financial reasons."
Usmanov, 59, has an estimated fortune of some £18billion and maintains his long-term ambition is to take a controlling interest in Arsenal, where American Stan Kroenke is the majority shareholder.
Speaking to CNBC from Moscow, Usmanov said: "I want to take this opportunity to just reaffirm that in order to help the team, we would be ready to buy more shares, to buy control, to buy all shares.
"We are ready to do all that we can in order to help the company, in order to consider any form of co-operation or ownership with the team.
"If I have a big stake in Arsenal of course I have my opinion what we must do, for example in the commercial side there are many questions over the effectiveness of the commercial side of Arsenal today, but we will see, we will wait and maybe when I wake up some day I have this Arsenal club.
"I always tell Mr Wenger he is one of the best coaches and football managers in the world, but I openly admit he has many, many difficulties to contend with."