Johnson lifted the Rugby World Cup in 2003 as England captain when Woodward was the team’s manager.
Legendary lock Johnson, after being parachuted into the post of England manager in 2008 with no previous coaching or management experience, resigned on Wednesday.
It followed a disappointing World Cup campaign where the team failed to reach their stated goal of a semi-final spot after a last-eight loss to France.
Woodward said he felt “sorry” for Johnson, adding someone in England’s governing Rugby Football Union had to be accountable for the decision to put a novice boss into such a high-profile job.
“I’ve no wish to coach England again,” Woodward, now the director of sport at the British Olympic Association, told Sky Sports on Thursday.
“I’m totally committed to the BOA,” Woodward added ahead of next year’s London Olympic Games.
Former Test centre Woodward, who like Johnson played for Leicester, said he’d urged his old skipper not to take the England job when Brian Ashton was forced out after the 2007 World Cup.
“I actually said `you should come to Leicester, spend four or five years there and earn your stripes,” Woodward explained.
“Basically I feel quite sorry for Martin Johnson because if you are asked to coach England you are going to say ‘yes’.
“Let’s be brutally honest, he had no coaching experience, no managerial experience, so it was a huge risk by those who put him in.
“I just don’t feel they put anybody alongside him to help him, to negate that risk, to make sure that the risk was worth taking.
“We’ve just allowed a rookie manager to just run his own ship for three and a half years without any real analysis, assessment.”
The RFU, who’ve lost a chief executive, a chairman and now the manager of their flagship side within a matter of months, would like to get a successor to Johnson in time for the start of the Six Nations in February.
The search is being led by Rob Andrew, the RFU’s elite rugby director, who is now aiming to work alongside the fourth England head coach of his five-year tenure at Twickenham.
Since Johnson quit, renewed attention has focused on Andrew.
Woodward urged the RFU not to rush into a decision, saying a caretaker manager could oversee the Six Nations as England looked to rebuild ahead of hosting the 2015 World Cup.
“We can’t get it wrong, because I think we have got this one wrong,” Woodward said.
Former South Africa and Italy coach Nick Mallett has ruled himself out, with Northampton boss Jim Mallinder the leading English candidate.
Graham Henry, who stepped down as New Zealand coach after guiding the All Blacks to World Cup glory last month, and former Australia coach Eddie Jones have been linked with the role.
