The Owls took an early lead in the lunchtime kickoff at Elland Road, but two goals from Luke Varney ensured a home win.
The Wednesday manager told Sky Sports News: "We should have won. We switched off for 15 minutes and allowed two goals which we should never have allowed. You can't give somebody free headers in your box.
"It's frustrating because they caused us no hassle, apart from a 15-minute period. We had a few injuries and had to change things around but we made some basic errors.