The Springbok skipper branded Johnson "one of the dirtiest captains in world rugby" in what he believed to be an off-the-record chat with a South African newspaper journalist, comments he has since apologised for, but Woodward dismissed the taunt as just part and parcel of modern rugby.
"We see such comments as positive feedback – banter – when you read about it you just have to smile," said the wily England coach.
"The reaction in the team-room was just one of amusement. Sledging is common-place these days and we have all been smiling about it."
Woodward said his players had grown accustom to the flak and, as part of a team the world loves to hate and longs to beat, had learnt to except it.
"It's going to get a lot worse, we're still a week away and it's already started. It's part of the baggage you carry by being the England rugby team," he said.
"I couple of years ago we tried to change it but you just can't – I've occasionally fired a few barrages back and when I do that everyone goes mad about it. Meanwhile we just sit here and politely cop this rubbish.
"But I'd be annoyed it any of the England players retaliated, we just have to take the higher ground."
Woodward, who names the side to play Georgia on Tuesday, will put his squad though their paces during a series of short training sessions building up to Sunday's opening game.
The sessions will be closed to the public and the team's privacy will be enforced by England's own security personnel, but Woodward denied that such measures are overly cautious.
"We will have security patrolling the fences because secrecy is very important part of the game," said Woodward.
"It would be a massive advantage if I was able to watch opponents train and rehearse moves so we are doing everything possible to prevent such a situation arising without being overly neurotic about it."
The security staff will have a day off on Friday, as will the England players who will be resting up prior to their opening game, but Woodward has no fears that his charges would be distracted by Perth's myriad appeals.
"Gone are the days of the mass outing or organised tour," concluded the coach.
"My players know how to approach big games so it will be just a question of putting our feet up. We're not here to enjoy ourselves – we're here to win."
By Andy Jackson