The hosts were 3-0 up within 15 minutes after goals from Paul Smyth, Jake Bidwell and Idrissa Sylla.
The recalled Sylla got his second - a penalty after Tom Lees had fouled Bright Osayi-Samuel - eight minutes into the second half.
Fernando Forestieri, starting a game for the first time since August, pulled a goal back for Wednesday just after the hour mark.
Atdhe Nuhiu headed in Liam Palmer’s right-wing cross nine minutes later to test Rangers’ nerves, but their early blitz proved decisive.
“In the first 15 minutes we were not in the game,” said Luhukay.
“It was not good defending and we were only reacting to what QPR were doing. That first 15 minutes cost us the game. On the ball I thought were were good. But when you see the 90 minutes back we lost it in the first 15 minutes.
“I have no explanation for that. It is disappointing and we have never started as badly as that. We let crosses in. You must block the crosses and also defend in the 18 yard box.
“We must be better. We started too late. After 20 minutes we came back into the game but when you’re starting after 20 minutes you cannot win.
“The team did not give up and we had chances. They kept fighting, got two goals and we had a chance for a third goal but luck was not on our side.”