While Trinity boss Chris Chester reflected on what he felt was his best win at the club, Furner was left to rue a missed opportunity.
Rhinos remain second from bottom in Betfred Super League, ahead of London Broncos on points difference after again failing to build on a positive performance, following the Good Friday win over Huddersfield Giants.
Rhinos hit back from 12-0 down to level the scores at half-time, but Trinity - missing 12 senior players - ran in 14 unanswered points before Leeds managed a late rally.
Furner said: “We did a really good job to come back from 12-0, playing some decent football.
“In the second half we talked about doing the same things - stick to the game plan.
“I thought we went away from it in the second half, in particular at the start.
“It wasn’t good enough. We nearly ran them down again towards the end, but just ran out of time unfortunately.”
Wakefield did not have a play-the-ball in Rhinos’ 20 in the first-half, but scored one try from an error and another off an interception.
Furner felt that “gave them energy” and admitted Leeds weren’t clinical enough near their opponents’ line.
“In the back end of the halves I thought we’d be able to get on top,” he said.
“In the second half we [conceded] two really poor penalties. You can’t put the team in that situation.
“That kept putting energy back into Wakefield’s defensive line and I thought our execution on their tryline was poor.”
Furner added: “I am disappointed.
“I still feel we are learning, but you want to be learning of those types of games and grabbing the two points.
“We need to learn from that second half, but we need more actions and a bit more control from our senior players.”
Rhinos were without star centre Konrad Hurrell who suffered a hamstring problem against Huddersfield, but Trent Merrin returned after compassionate leave in Australia.
Of Hurrell’s injury, Furner said: “It’s not as bad [as Rhinos feared], but I am not sure if he’ll be ready for Sunday against Hull KR.
“It was good that Trent was back, but he had only just got off the plane. I thought he did a tremendous effort.
“We lost a bench man. Wellington [Albert, who suffered a head knock] has been pretty good for the team so that was a bit of a loss, but Wakefield had their injuries as well.”
Teenager Owen Trout man his Super League debut and played the full game against his hometown club.
“We’ve got some young players in there and having that experience and those opportunities is only going to be better for the future,” Furner stated.
“Harry [Newman] probably has some learning to do on that left-edge, but I like the young players bringing that energy and going out and doing their best.
“That’s what I ask from the younger players and I think we got that.”