The game is England's first since they lost their two-Test series in New Zealand in July.
Borthwick told The Rugby Paper, "Of our last 15 games, we've had two at Twickenham.
"Seven of our next nine are at Allianz Stadium. And we want to make sure this is a place that our players enjoy playing, that our fans enjoy coming, because they're seeing an England team performing and an England team winning."
Borthwick backed his players because they had achieved many good things but added that games had been lost when they shouldn't have.
"You can accept inexperience, but you have got to learn the lessons fast.
"We were in a winning position in Dunedin, and we didn't win, and then we got ourselves into a winning position in Auckland, and we should have learned the lessons from the week before, and converted that, and we didn't in the final quarter."
England needed to be more consistent in getting into a position to win games, something he felt they had been doing better in their most recent outings.
"There was a period, not so long ago, where we weren't competing against the top four, now we're competing, but I want to make sure we get the job finished at the end."
England are having a camp in Girona this week as Borthwick ponders his team to take on the All Blacks and what effect injuries will have on the shape of his side.
"It becomes what we need tactically at the start of the game, what we want at the end of the game and people getting the job finished. Those things become part of the selection process."
Meanwhile, former England and British & Irish Lions back Jeremy Guscott said in his Rugby Paper column the All Blacks will have to be at their best to win, especially facing England, Ireland and France on consecutive weekends.
"In 2015, we would have expected New Zealand to win all those games with something to spare. They would have been able to mix and match their starting 23, or even put a second team out, and still win comfortably – whereas this time out, they will absolutely have to be at their best.
"A big element with New Zealand is that for a long time, they appeared to other teams to be invincible, but now all the top six teams in the world think they have a good chance to win against them – so that barrier is well and truly removed.
"However, even with players who are not so dominant in their positions on the international stage, and with a new coaching team which is still finding its way, I see enough in New Zealand to believe that at their best they can beat anyone in the world in any given match."