Chris Chester’s side trailed their title-chasing opponents just 13-10 with 14 minutes to go but conceded two late tries to lose 25-10 on Thursday.
A yellow card for Scott Grix after Matty Ashurst had also received one in the first period did not help matters but Trinity matched Wigan for long spells.
Centre Lyne said: “We gave away a lot of yardage penalties which has been a problem the last few weeks.
“Then obviously there was the two sin-binnings which didn’t help combined with not completing sets well which took its toll in the end. I think we were our own worst enemies.
“But that performance still gives us a lot of confidence especially as we had a few big boys missing as well.
“Wigan are a really good team. We feel if we can tidy a few things up we can really challenge the top-four next year. I think Wigan are the best in the comp’ at the moment and we ran them close.”
Wakefield were just two points behind fifth-place Huddersfield Giants after beating them the previous week and hauling in their West Yorkshire rivals remains their main target.
Trinity host Challenge Cup winners Catalans Dragons on Friday and Lyne admitted: “We are desperate for that fifth spot.
“It’s prize money for the club and every penny counts for a club like Wakefield.
“We finished fifth last year and we want to emulate that.”
Ex-Hull FC centre Lyne, 25, is enjoying arguably the best campaign of his career and hopes to represent England Knights in Papua New Guinea this autumn.
“I am loving it here,” he said.
“I’ve re-signed for another four years and can’t speak highly enough of it while hopefully I’ll get on the plane, too, at the end of the season.”