"It is an almost impossible job," Gibson told BBC Radio Five Live.
"If you do your job properly as chief executive at the FA then, more likely than not, you will come into conflict with the board.
"They should have an independent chairman, a chief operating officer and a leadership team below that."
Gibson offered his resignation from the FA on August 1 - the same day as Palios.
It came in the wake of newspaper allegations concerning Palios and England boss Sven-Goran Eriksson, as well as claims that there was an attempt to broker a deal with a Sunday newspaper.
