Woodward has also warned England coach Stuart Lancaster "one stupid tweet" from any of his players could derail his team's World Cup bid on home soil.
The 2015 tournament hosts launch their campaign against Fiji at Twickenham on Friday week, and Woodward has revealed he has handed current boss Lancaster some words of advice ahead of the global battle.
Woodward categorically cites social media as the chief pitfall.
"It's the new enemy," the 59-year-old said, speaking in this week's Radio Times.
"We didn't have to worry about it in 2003."
Woodward shined a light on the advice he had given Lancaster.
"Don't let the players be distracted. It could be the media, their family, sponsors, ticket requests, anything.
"One stupid tweet, one ill-judged video out on social media - if you allow one player to be distracted, it can affect the whole team, and it can all come tumbling down."
England have reportedly handed their World Cup squad social media guidelines, keen to avoid any unnecessary distractions.