The coach of England's World Cup-winning team in 2003 launched a withering attack on the game's administrators and the process used to appoint former manager Martin Johnson.
Writing in the Sunday Times, Woodward said: "Martin Johnson has gone but has anything else changed?
"I have a serious fear that all the mistakes made at Twickenham, which have reduced England to something of a laughing stock around the world, are about to be made again and four more years will then be wasted.
"All the people who appointed Johnson - a man who had never coached anyone at any level - are still in place. There is nobody who understands elite performance and rugby at the very top. Equally disturbing, the same people are going to appoint the next coach."
Woodward singled out elite rugby director Rob Andrew and his role in the process.
"He refused last week at a press conference to take any responsibility for the past shambles," Woodward said.
"Then he told the media that he took no responsibility for anything that happened at the World Cup.
"So why does he have responsibility for choosing the new coach? The absolute key question for me is whether he has the skill set to appoint the new coach. Experience says he does not."
Woodward insists Johnson should not have been handed the job in 2008 due to his lack of experience.
"He has the qualities to be an outstanding coach, just as good as he was a player and captain, but even he cannot learn this job at the very top level on the hoof," he said.
He states a preference for an English coach to get the job, naming Jim Mallinder, Richard Cockerill, Toby Booth, Conor O'Shea, Neil Back and Mark McCall as contenders, while also suggesting that Alex King and Mike Catt should come into consideration.
"An English coach would know the country and the culture," he said. "England have so many coaches, so many resources - if so enormous a rugby country cannot produce a contender, what does that say about rugby here and our coaching development programmes?"
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