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Johnson's men gave away 10 penalties in all, six of which were slotted over by fly-half Giteau and one by captain Stirling Mortlock - a monster of a kick from just inside the halfway line.
"We didn't make them work hard enough to score 28 points," said Johnson, who skippered England to victory over Australia in the 2003 World Cup final.
"We gave them eight penalties and they scored seven and that makes it very difficult.
"We went a little bit off script. Guys in the heat of the battle went with instinct and what they do week in, week out instead of sticking to what were trying to achieve and that was the frustrating thing.
"If you're doing one thing and 14 guys are doing something else that's when you get turnovers and mistakes - and we made far too many of those to keep the pressure on.
"We've got to trust ourselves and back ourselves.
"At half-time we really were where we wanted to be but in the second half we just didn't keep the pressure on.
"There was a tremendous amount of restarts and they slowed the tempo of the game down.
"But, you know, they've won by 14 points and they know how to win Test matches. They'll be ecstatic and rightly so."
Fly-half Danny Cipriani has been billed as England's next big thing, but he flattered to deceive at Twickenham, missing two conversions and an easy drop-goal chance early in the second half.
Two breakaways which failed to reap any points showed flashes of the 21-year-old's potential, however, and Johnson refused to criticise his performance.
"I think he's learning all the time what Test match rugby is all about," he said.
"It's about how you handle the pressure of the field.
"We're together five weeks and then he's back to Wasps and will be playing in Europe.
"It's about finding out what being a full-time rugby player is all about. There are a lot of them doing that."
Johnson added: "We'll get together on Monday. The guys will be sore, they'll be frustrated, they'll be disappointed.
"But we've got to bounce back and put things right as best we can and be here next week."