Respects were paid to the England World Cup-winning captain over the weekend to mark the 20th anniversary of the defender's death at the age of 51.
"The FA has been criticised over its treatment of Bobby once he retired," the Daily Mail quotes Bernstein as saying. "It saddens me that this is the case and while I am not privy to exactly what happened, it is clear the organisation could have done more.
"If Bobby were alive today I am sure we would have asked him to be the chief ambassador for the FA in its 150th anniversary year."
Moore passed away when he lost his battle with bowel cancer.