England were carved up by the world champions who scored four tries in a rampant first-half display at Waikato Stadium to take a 29-6 lead at the break.
Julian Savea, who eventually finished with a hat-trick, was on the board twice in the first nine minutes. Halfback Aaron Smith added two more as England found themselves chasing shadows.
"I guess they fell into the trap we have the last couple of years when it came to the end of our year. You've got one eye on your break," said Jane, who had a hand in three of the four tries.
"In the first half maybe they were looking at a few weeks off because it had been a long season. We took advantage of that.
"We did the same thing a couple of years ago (when we lost to England) and Ireland last year and made life hard for ourselves because we were looking at the summer. I guess they did too."
Jane certainly had his mind on the job after a couple of below-par performances in the first two Tests of the year.
On Saturday he was superb. He was steady under the high ball, scooped up a loose ball in the build-up to Savea's first try, showed great footwork to get past England winger Marland Yarde to set up Smith's second try and then fended off another Englishman as he sent Savea in for his hat-trick after the final siren had sounded.
"I'm thankful that I'm on his team," Jane said of the big left winger, who has now scored eight tries in four Tests against England and has 22 tries in 22 Tests overall.
"The work started from the set-piece. We managed to draw their players in and all of Jules' tries were just a jog in. When you're a winger and you can stroll over it shows that guys are doing their job."
All Blacks coach Steve Hansen felt the "real Cory Jane" had returned in Hamilton.
"He's been guilty of trying too hard since coming back from his ankle injury," Hansen added.
"He is an effervescent sort of player and when he's in that form he's a handful. He proved to be a particular handful tonight."
Jane said it was just a case of him doing his own job.
"I went into it like the old Cory, just relaxed. I didn't try and do too much. My mind wasn't cluttered. I just responded to what was in front of me," the 48-Test veteran said.
"It's surprising how well you can do when you're down and everyone is giving you a boot.
"You either respond by doing your job or you let it get to you. I was pleased I was able to take a step in the right direction."