The scale of England's dominance was further emphasised by the fact they made 11 line-breaks to Scotland's three, and made 597 metres in the territorial battle to their opponents' 225.
All in all, the numbers told the story that Scotland were a distant second best in every area except the set-piece.
"We are disappointed," Johnson said firmly. "These are areas we have to work on. You can go on about how you want to play rugby, but if you don't get the contact area right then you can dream all you like because those fairytales won't come true.
"We lost the battle for field position because of our inability to deal with them. We were poor in the contact area. It's simple."
Scotland's rucking game is a traditional area of strength, but they were given a lesson in how to secure and use quick ball by their English opponents. Johnson acknowledged the importance of that phase of play, but was blunt about the fact Scotland had simply not been good enough to match their hosts.
"We spoke about the improvements that were needed in our game when we first came into camp," the coach said.
"Look at the best teams in the world – they are all the best in the contact area, with or without the ball. Everyone looks at their great rugby players, but they can't be that if they are not getting quality ball.
"We just didn't get it right. A lot of it is position, a lot technique. The fact is we didn't do our part right.
"We were slow in our line speed coming forward, so we were constantly going back. We talked about it, but we didn't do it.
"There's no panacea. It's just good old-fashioned hard grunt. The reality is that there are improvements needed in our game across the board, at all levels.
"We showed great endeavour in some aspects of the game. I don't question for one minute the resolve of the boys. They are a fantastic bunch of kids and good players, but we've got to work on areas of our game. We're deluding ourselves to think otherwise."
Kelly Brown, the Scotland captain, backed up Johnson's words, admitting that losing the breakdown battle had been the root of most of the team's problems.
Brown said: "England were able to play the game in our third. They won the gain line. If you are on the back foot and playing a lot of rugby in your own half it is very hard to compete.
"We knew that we had to get off the line. Because we didn't, England were able to get fast ball and that was a big advantage.
"But we need to get back up, it's as simple as that. You can go away and feel sorry for yourself, but that won't achieve anything. We have to learn our lessons, work hard and then come out firing against Italy at Murrayfield next Saturday."
Stuart Lancaster expressed satisfaction with his team's display, but conceded that mistakes were made and there is still scope for improvement.
"I think people underestimate how long it takes to pull a team together," said the England coach, whose first game in charge was the victory over Scotland at Murrayfield a year ago.
"We needed to create a new sense of direction for the players, and I think we've done that. Over the past 12 months we've had some ups and downs, but we've learnt as we've gone on."