Rhinos led 4-0 early on, but Trinity stormed back to lead 22-10 at the break and Leeds’ only second half points came after Trent Merrin had been sin-binned for dissent.
It was Leeds’ fourth defeat from their opening five Betfred Super League fixtures and Furner said: “There were some system breakdowns defensively that were not good enough.
“We conceded too many points in the first half.
“At times we were good with the ball, but there are two parts to his game.”
Furner paid tribute to Trinity as a “good side” and admitted Leeds did not contain their potent left-edge.
He felt Leeds defended better on their line after the interval, but added: “Wakefield are quite big and strong and we didn’t handle that. We allowed them to play too fast on our tryline.”
Wakefield coach Chris Chester was in a far happier mood afterwards, describing it as a “special night”.
He reflected: “It is always tough when you come here. In the first 10 minutes I thought we were in for a long night, but we slowly got ourselves into the game I thought we were dominant from the 10th minute until the 80th.
“In terms of performance it’s not far from being our best one.”