Johnson said his players had given their all until the final whistle but admitted he faced a trying week ahead of next Saturday's match against the number one side in the world, New Zealand.
"It's about character this week. It's a question of getting heads up and all of us as a group getting on with the job," he said.
"They're our best players and we have to have faith in the guys we've got there.
"We're going to get sniped at by the media, and rightly so, but we have to take it on the chin, bounce back next week and play our hearts out."
International rugby is all about fine margins and we made too many errors
England captain Steve Borthwick
England captain Steve Borthwick said they were "tremendously disappointed" by the heavy defeat.
"The changing room is a very quiet place," added the Saracens second row.
"International rugby is all about fine margins and we made too many errors. Credit to South Africa - their work around the breakdown, their defensive work and the way they took their chances was a lesson to us.
"We want to be better and we want to improve. All we can do is work hard, study the tape of what happened today and put it right next week. We had plenty of ball, we've just got to use it better."
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