"We had that belief to beat them and a mentality to attack. It was all about going out to attack them," Best said.
"This modern-day All Blacks side is so difficult to beat. They have so many attacking weapons, and they will always score tries.
"We found that out a couple of weeks later in Dublin that if you do not score tries against them it is very hard to beat them."
New Zealand avenged the Chicago defeat 21-9 in Dublin two weeks later.
Best said that the Lions had to emulate Ireland's tactics and suffocate the All Blacks with constant pressure to win.
"You have to put pressure on them, getting in their faces, quick line speed, putting them under pressure," Best said.
"There is more than one way to skin a cat. Whatever way we go, it is important everyone buys into it and adds something to it. Maybe we will do it slightly differently to Chicago."
The Lions start their 10-match tour against the New Zealand Provincial Barbarians in Whangarei on June 3. They face the All Blacks in the first of three tests on June 24.
Hooker Ken Owens will face a fitness test before the tour after being ruled out of PRO12 club Scarlets' play-off game on Friday with an ankle injury.
(Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford)
