After trailing 10-0 inside half an hour, Wakefield cruised into an 18-10 lead at the interval, but the wheels came off in the second period and they finished well beaten, despite facing 11 men in the closing stages.
“It was pretty poor,” admitted Poching of his team’s second defeat in his six games in charge.
“Leigh were fantastic and deserved the win.”
Tries by Adam Sidlow and the first of a hat-trick from Ryan Brierley - who also booted three conversions - rattled Trinity early on, but Wakefield came up with an impressive response, going ahead within nine minutes of the hosts’ second touchdown.
Reece Lyne kick-started the fightback with an extraordinary try, putting boot to ball twice - the second a lovely chip over full-back Brierley - before gathering to touch down.
Moments later, Kelepi Tanginoa ran through from Jacob Miller’s pass and then Brierley spilled Mason Lino’s high kick and in the resulting set Dave Fifita rumbled his way over the line and Lino’s third goal made it 18-10.
Leigh cut the gap just seconds after half-time when Iain Thornley made a break down the left and Brierley was in support to score his second.
James Batchelor had a touchdown ruled out for a double-movement before Brierley completed his hat-trick with 22 minutes left, though Sam Stone’s pass looked forward.
Kay - for a forward pass, though Trinity received a penalty from it - and Batchelor, after an obstruction, had tries disallowed in quick succession and soon afterwards Leigh went two scores clear through Stone.
Centurions were reduced to 12 men when Rob Butler was sin-binned for a foul on Chris Green and then Brierley followed him for a professional foul after a try-saving tackle on Reece Lyne, moments after the full-back had brilliantly kept Innes Senior out.
Poching added: “I didn’t see this coming. “We got ourselves some field position in the first half, but the attitude we went into the game with we weren’t quite able to get rid of and correct.”
Leigh Centurions: Brierley, Elliot, Thornley, Hellewell, Logan, Bell, Mellor, Sidlow, Hood, Butler, Stone, Thompson, Whitbread. Subs Ashworth, Mason, Gerrard, Ellis.
Wakefield Trinity: Hampshire, Kershaw, Lyne, Arundel, Senior, Miller, Lino, Green. Kay, Battye, Batchelor, Tanginoa, Crowther. Subs K Wood, Arona, B Walker, Fifita.
Referee: R Hicks (Oldham).