England's World Cup failure and the aftermath has been "shambolic", says ex-RFU chairman Martyn Thomas.
Stuart Lancaster, 46, left his position as head coach on Wednesday after England became the first sole hosts to exit a World Cup at the pool stages.
"We won in 2003, 2007 was not great, 2011 got poorer and, as for 2015, we have come off the precipice," Thomas told BBC Radio 5 live.
"To be a successful national team coach you've got to have an X factor. "
England's World Cup exit saw them become the worst-performing host nation in tournament history.
In his Daily Mail column, England's 2003 World Cup-winning coach Sir Clive Woodward wrote that Rugby Football Union chief executive Ian Ritchie should also be held accountable.
But Ritchie, who says he accepts responsibility for the World Cup disappointment, believes he is still the right man to lead the search for a replacement of "proven international experience".
"I'm the chief executive, I run the organisation, of course I feel personally about what's gone on," said Ritchie.
"It's equally important that I continue to deliver for the organisation and move it forward."
Lancaster's departure followed a review into England's performance, which involved an RFU panel taking "extensive feedback" from some members of the squad and all 12 directors of rugby at Premiership clubs.
Ritchie said the RFU's focus would now be on taking "sufficient time" to find the right person to succeed Lancaster.
"The RFU need to look at the organisational structure as it hasn't worked in successive four-year periods since Woodward," Thomas told 5 live. "How do we do ensure this isn't going to happen again?
"One answer certainly is to appoint the right individual, also to look at the structure and how the individual we appoint is managed, so that he is managed on a regular basis throughout the four-year cycle.
"Stuart Lancaster is a really nice gent. He is very media savvy, very public savvy, a professor of rugby."
Lancaster, who only signed a six-year deal in 2014, was made permanent coach in 2012 and won 28 of his 46 games, but failed to win the Six Nations.
"It is so wrong that Lancaster alone seems to have been responsible for England's failure," said Woodward in the Daily Mail.
"Those responsible for his appointment, and who have backed him and been happy to reap praise in the good times, should be looking in the mirror today and feeling very uncomfortable over what has happened."