Johnson stood down as England manager on Wednesday's after England's disappointing World Cup campaign, which ended with a quarter-final defeat to France.
England's World Cup-winning captain was recruited by the RFU in 2008 despite having no coaching experience and Woodward, who led an England side captained by Johnson to World Cup glory in 2003, believes he should have been given greater support.
Rob Andrew, the RFU's elite rugby director, was Johnson's immediate line manager and Woodward questioned why Twickenham's top brass allowed England to fail at the World Cup before taking any action.
"Basically I feel quite sorry for Martin Johnson because if you are asked to coach England you are going to say 'yes'," Woodward told Sky Sports.
"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.
"He's an iconic figure, he's a brilliant guy, but that didn't seem to fit very comfortably with him.
"The England players need to know the RFU is putting in the very, very best because you only get one shot at this.
"We've just allowed a rookie manager to just run his own ship for three and a half years without any real analysis, assessment.
"I think that is so so wrong and someone should really be accountable for that."
On Thursday, Andrew presented his review of England's World Cup campaign to the Professional Game Board, which will not make any recommendations to the RFU board until November 30.
It is understood Andrew's own role in the England set-up was set to come under scrutiny in a meeting chairman Ian Metcalfe described as "robust".
Woodward questioned the need for such an extensive review process, arguing Johnson's superiors should already know what issues existed within the England squad.
"That's why I'm a little bit baffled," Woodward said.
"They've lost in the quarter-final, we've now got reviews... how long ago since the World Cup?
"If you're on top of this, the people who are making those judgments should be reporting back to the management board at Twickenham almost within days.
"They should know exactly what's going on within the England team, not just with Martin but with all the coaching team. They should know inside out what is happening. Then you can make judgements.
"If you are really on top of it then you should make these changes, you haven't got to wait until the World Cup.
"We shouldn't have to wait for a bad situation happening and then have this reaction."
Andrew will now oversee the recruitment of Johnson's replacement, the fourth England head coach during his five-year tenure at Twickenham.
Woodward urged the RFU to take their time, set up an interim England management team to take care of the Six Nations and concentrate on making the right appointment.
The next England coach will be charged with leading the team into the 2015 World Cup on home soil.
Woodward believes the appointment should not be made by committee, but on the recommendation of one man who has the faith of the incoming new chief executive.
"We've got this huge issue coming up now, who is the next England coach? What are the right criteria?
"We can't get it wrong, because I think we have got this one wrong. In Martin's own words, it's not gone well."
Woodward is not in the frame to return to Twickenham as England coach - but he remains a potential candidate to run the RFU's Professional Rugby department.
Andrew is currently fulfilling that brief but he has not been officially appointed into the position.
"To be very clear I've got no wish to coach England again," said Woodward, who is currently performance director at the British Olympic Association.
"In terms of post-Olympics, I think you'll find in British sport there's going to be a huge amount of changes, there will be all sorts of opportunities all over the place."
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