Easterby, a 65-Test player for Ireland, has been their forwards coach since the 2014-15 season and had been a witness to the transformation under New Zealand coach Joe Schmidt.
"As a team we were often gallant losers in my time as a player; we pushed teams close every now and then. We had the odd maybe two, or three, or four game-winning streak against the top sides and then maybe we'd fall over," Easterby said.
Schmidt had provided the formula to success. He had especially worked on consistency in performance with a resulting lift in confidence.
That had allowed them to beat the All Blacks, to win in South Africa and Australia, to win the Six Nations and Grand Slams.
The side had developed confidence in their game plan and defence structure provided by Andy Farrell.
"I think there is a combination of different things that have come together," Easterby said.
"A lot of them all have to come together at the same time, and sometimes when you don't quite get everything right then sometimes we're not good enough.
"So we have to be at our best, or close to our best, on Saturday and if we are then we'll push them all the way," he said.
At the same time they needed to be wary of the threats the All Blacks would bring and Schmidt, with his New Zealand background, was in a position to impress on the side what it took to beat a team like the All Blacks.
"That filters through the group as we go through the week and the confidence that we gain has been shown in a couple of performances that we've had against them," he said.
"They have been the number one side, maybe not all by name but certainly over the last few seasons they have been the consistently the team to beat. You know that you're always in a hell of a game and to beat them you've got to be at your best.
"That provokes excitement, it provokes a little bit of anxiety. You've got to get nearly everything right and I think that drives this group.
"They're driven by a number of things but the challenge and the demands they put on themselves shows that we can raise our game for the likes of New Zealand, South Africa, England in Twickenham, two Test wins in Australia, those types of challenges have often been met by this team and this Saturday is no different," he said.
"New Zealand are a big threat and I think that we can also have an impact on their set piece. As much as it's vital that we get on the front foot and give ourselves the opportunity to win front foot ball at scrum and lineout, the pressure will clearly come on at times. But we have the ability to put the pressure on them as well," he said.