Woodward guided England to the 2003 World Cup title in Australia when Jonny Wilkinson's drop goal sealed victory over the hosts in the final.
Such success contrasts greatly with the miserable campaign by the team in New Zealand last autumn, which ended with a quarter-final defeat by France and also featured a number of off-field controversies.
Johnson subsequently stood down in November, to be replaced by Stuart Lancaster as interim head coach.
Woodward believes Johnson paid the price for failing to manage what was happening both on and off the pitch.
He told the Independent on Sunday: "Johnno did it his own way as every coach does.
"I am not saying the way I did it was right or wrong but it would have been different.
"Okay, I was successful but it would be wrong to say that was the blueprint.
"But you are judged on results off the pitch as well as on it and you have to get that right."
Woodward, who has many times been linked with a return to Twickenham, is supporting Lancaster and believes England will emerge from what has been a bleak spell.
He added: "You wish him well. He's got a great opportunity and I just hope he picks the team that every England fan says, 'Wow, I am looking forward to watching this'."
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