Woodward, who coached the Lions on the 2005 tour of New Zealand, called time on his hugely successful England career six years ago.
His resignation came a year after the former Lions centre had led England to World Cup glory in Australia.
Woodward publicly criticized the RFU in his resignation speech, blaming his former employees for failing to give England the support needed to move forward in the aftermath of their World Cup triumph.
But the 54-year-old has now publicly stated that he was wrong to make those comments, insisting that he should have taken the advice of his wife Jane and left on a more amicable footing.
"Ninety-five per cent of Jane's advice I have taken, and five per cent I haven't," Woodward told the BBC's Desert Island Discs.
"The one time I didn't take her advice, which I regret, is when I left the England job.
"She briefed me before the final press conference. She said this is the time to thank everybody, that we had been incredibly lucky, and reminded me that I had resigned and that the RFU did not want me to go. So, that's what I decided to do. It lasted 30 seconds. Something was said and I just tore into them."
Sir Clive made his frustrations with the England set up obvious for everyone to see when he personally criticized a number of individuals and the organization as a whole.
It left a sore taste in the mouth of the RFU and Woodward wished he had now done things differently.
"I went into them in terms of why I was leaving. It wasn't the right time to do that because without Francis Baron, Graham Cattermole and the RFU, I wouldn't have achieved as much as we did. They had supported me brilliantly.
"I had decided to resign. It wasn't the time for cheap shots, it was time to shake hands and move on.
"Jane was sitting in front of me and I could see her face going whiter and whiter, horrified at what I was doing. We got in the car afterwards and sat in silence for a minute.
"She looked at me and said, 'That's that. You have just burned your bridges. There is no way you will ever come back here. You may be right in what you're saying, but it was the wrong time to do it.'
"I got it badly wrong. I regret it now."