TOWN are out of the Pontin's League Cup after a second successive group defeat.
A virtual Academy side battled hard but lost to goals by Barry Corr and substitute Matthew Bowman at Hillsborough last night.
Following the 2-0 home defeat to West Brom last month, it means Town cannot be one of the two teams to go through to the knockout stages, even if they win their final group outing at home to Rotherham in four weeks time.
Coaches John Dungworth and Martyn Booty saw a tremendous effort from their young charges but they drew another blank in front of watching manager Peter Jackson and Sheffield-based centre-back Martin McIntosh.
Town were hampered, too, by injuries to defender Adam Wilson - who was helped off after twisting his right ankle - and Adnan Ahmed, who suffered another niggle with only 37 minutes gone.
With only four pros - Paul Rachubka, James Hand, Ahmed and John McAliskey - in the starting line-up, Town were restricted to just one dangerous McAliskey shot in the first half and went behind on 19 minutes when a left-wing cross was headed back for Corr to net from close range.
It was nip and tuck after that, but Town made a blistering start to the second half and were unlucky not to equalise.
Mitchell Bailey had a 20-yard free-kick well saved after a foul on McAliskey, while substitute Alex Hallam had a shot blocked in the box after a smart low cross from Hand.
Then young Lucas Akins joined in the fun, running past several defenders to set up Bailey for a cracking drive which fizzed inches over the bar.
Akins wasn't done, for on the next attack he flicked the ball over marker Rory McArdle and sent in a crunching volley which keeper Chris Adamson did well to block.
A goal then would have given Town valuable confidence, but it was Wednesday who extended their lead on 63 minutes after a handling error by Rachubka, who bravely blocked a follow-up shot from Burton O'Brien but couldn't stop the next effort from Bowman.
Town - Rachubka, Roberts (Broadbent 61), Hand, Skarz, Codman, Wilson (Hallam 30), Berrett, Bailey, McAliskey, Akins, Ahmed (Jackson 37). Subs not used: Booty, Eastwood.