The trio were coached by former Hurricanes Super Rugby title-winning coach Chris Boyd during his four-year tenure as director of rugby at Northampton, which ended in 2022.
Furbank told English media ahead of the Test that Boyd's mantra was about playing to space.
"You never mention the word risk with him. It was always a decision, and if you're making the right decision, whether on your line or the opposition's line, he will back you to do that.
"It's about seeing that decision in the first place and backing yourself to execute it.
"He gave us a sense of freedom to go and play. Some coaches make you worried about making mistakes, whereas this was a new philosophy and one that helped the young guys coming through.
"The All Blacks are happy to go from anywhere on the pitch. If they see an opportunity, they're going to back themselves, and I've been lucky enough to play at a club that has implemented a similar sort of thing."
Furbank said England would need to maintain the momentum they found in the latter stages of the Six Nations in their games with Ireland and France and against Japan en route to New Zealand.
"There's a sense of seeing opportunities and backing ourselves to take them.
"We've got a very exciting young backline who want to be able to do that, and the coaches have fully bought into that as well.
"We've got some very good and accurate kickers and wings who are pretty happy going and getting the ball back in the air. That's a big strength of ours that's clear to see.
"We've added some good layers on to our attack as well. We've got a better understanding now as a group of where we want our attack to go, and what we want our attack to look like."