And to compound their misery Daniel Cleary, one of their better performers, was sent-off near the end at Hillsborough.
"We were not at the races, from start to finish," reflected coach Richard Beale. "We were low on intensity.
"It was a shame after doing so well at Ipswich on Monday (Blues won 3-2), but we just couldn't get a grip of the game at any stage."
Blues fell behind to a 25-yard free-kick struck by Claude Dielna in the first-half and the Owls added a second through Warren Clarke after the break.
Connal Trueman pulled off some good saves for Blues and Cleary (pictured) was unfortunate to receive a straight red card, Beale revealed.
"It was a very soft dismissal. Dan went in for a tackle and the referee said he followed through. Their lad falls on the floor and Dan falls over him. It was unjust; Dan was excellent all game."
Blues: Trueman, Caddis, Seddon, Cogley, Cleary, Baba, Cooper (Popa 70), McDonald, O'Keeffe, Lubala (O'Neill 60), McFarlane. Not used: Martin, Weaver.