The Gunners fell to a 2-1 defeat to arch rivals Tottenham, a result that leaves them five points outside the top four with 10 games remaining.
Brady insists that both staff and supporters are still behind the Frenchman and has encouraged the board to back him with the funds to return Arsenal to their former heights.
"I think he should be given that chance," Brady told the Daily Mail. "From where I am in the club I don't think there is any pressure on him - I think the board are 100 per cent behind him.
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"The majority of the fans are behind him, the staff are behind him and I think the board are behind him. So we wait to see what the future brings."
Brady went on to state that, if the proposed Uefa financial fair play rules are enforced, the Gunners would be at a great advantage.
"Now that we are in a very strong financial position, I hope the financial fair play thing kicks in," he continued.
"If that kicks in and you're only allowed to spend what you make it will put us in an even stronger position."