Borthwick told his side after the Tokyo win, "The performance level will need to rise as we face New Zealand. The discipline - you can't give that number of penalties away, we know that.
"You can't give New Zealand the space we gave Japan today.
"The team had one session in England before we flew, and we had one proper session in Japan getting over the jet lag, so producing that off a couple of sessions together has been very impressive.
"But we will need to go up several levels, and I expect us to go up several levels when we face New Zealand."
England conceded 15 penalties in their 52-17 win over Japan and had lock Charlie Ewels red-carded—the first English player to be sent off twice in consecutive Test appearances.
Captain Jamie George said he was proud of the way England played.
"It was a tough game. The conditions were difficult.
"It was always going to be very difficult to come over here and get the result, but we're happy with that.
"It took us a little while to get used to the conditions but off the back of that we were efficient with the ball and moved the ball into space. We've got some talented backs with a lot of speed and we managed to show that."