Adam Reach had put the home side in front before Derby hit back to win with goals from Harry Wilson and Jack Marriott, with neither side adding to their tally after the break.
The opening goal came in the 12th minute when Barry Bannan’s lofted delivery into the area found Reach on the right-hand side and he slotted the ball past Scott Carson from a narrow angle.
But the Rams equalised in the 29th minute when Duane Holmes found Marriott inside the area and when his initial effort was blocked, the ball fell to Wilson, who volleyed it beyond Cameron Dawson.
Six minutes later, the impressive Marriott scored what proved to be the winner when he received the ball from Florian Jozefzoon and got in between two Owls defenders before advancing into the area and firing an early shot past Dawson.
After Morgan Fox headed over from Fernando Forestieri’s corner, Derby went close to adding a third in first-half stoppage time when Marriott’s first-time effort hit the bar.
After the break, Forestieri wasted a great chance after receiving the ball from Reach, shooting wide from a good position inside the area and Wednesday went close to an equaliser when Fox headed against a post.
“When you lose a game, you aren’t happy, you’re disappointed,” said Luhukay.
“I think in the first 30 minutes we played very good and came strong in the game. We made a good first goal from Adam and we tried to put pressure on.
“We lose after the 30 minutes. In five minutes, we gave away two goals too easily due to individual mistakes. We had a difficult time in the last 10 minutes before half time.
“The team gave everything to the last minute and I think there were two or three very good chances – Fernando had maybe the best chance to score and Morgan Fox’s header hit the post.
“It’s very frustrating when we look back on the last six or seven games and see how easy we give goals away.”
Sheffield Wednesday: Dawson, Baker, Lees, Hector, Fox (Penney 74), Reach, Pelupessy, Bannan, Matias (Nuhiu 73), Forestieri, Lucas Joao. Unused substitutes: Palmer, Onomah, Thorniley, Wildsmith, Pudil.
Derby County: Carson, Wisdom, Keogh, Tomori (Davies 46), Malone, Huddlestone, Holmes, Jozefzoon (Lawrence 77), Mount (Bryson 70), Wilson, Marriott. Unused substitutes:Waghorn, Johnson, Pearce, Roos.
Referee: Jeremy Simpson (Lancashire).