Woodward expressed concern over new director of elite rugby Rob Andrew's potential involvement with team affairs and the ongoing club v country row, and warned Robinson he would have to become a "control freak" to stand a chance of glory next year.
Woodward, who guided his side to success in Australia in 2003, said: "All I do know is we did it one way, which was by long-term planning and preparation.
"They can still win it because they have the players - they definitely have the players.
"Whether they have got the system in place, that is the question mark, but they can win it.
"The system worries me - that is why I left the job, and it has not changed in three years.
"But you have got to buck the system, hence you have got to become a control freak and you have just got to get it done - and you can get it done.
"We have proved it can be done, but you have got to make some tough calls and be very, very aggressive at times in getting things through.
"That is what they have got to be at the moment. They have got the players, they can certainly win it on ability, but they have got to take some really tough calls now."
Woodward, then working for Southampton Football Club, was a candidate for the job, but has since accepted the post of elite performance director for the British Olympic Association ahead of the 2012 London Olympics.