The Owls slumped to a fourth successive defeat, but the manner in which this team surrendered after half-time left Hillsborough stunned.
Goals from Teemu Pukki (2), Emi Buendia and Dennis Srbeny saw the Canaries cruise to victory, after goalkeeper Cameron Dawson had saved a first-half penalty to send the teams in at 0-0.
After shipping six goals in two games, defenders Michael Hector and Morgan Fox dropped out, to be replaced by Matt Penney and Daniel Pudil.
The Owls had a great chance to net early, but Josh Onomah blasted over after good work from Adam Reach down the left flank.
And the hosts had a major escape after five minutes. Tom Lees fouled Mario Vrancic in the box, but the latter's penalty was weak and Dawson was able to pull off a comfortable save.
Left-back Penney came close to providing another long-range stunner at Hillsborough, but his volley hammered against team-mate Steven Fletcher and into the arms of a grateful Tim Krul.
Reach was next to test Krul, but Onomah once again fired the rebound high and wide, before Barry Bannan's 30-yarder was pushed away by the goalkeeper.
But the Owls were behind on 50 minutes, a Moritz Leitner shot deflected into the path of Teemu Pukki, who slotted home.
And it could have swiftly turned into 2-0, Dawson alert to deny Pukki a second goal moments later.
Norwich did not have to wait long for that second goal. Terrible defending allowed Emi Buendia time to pick his spot and fire beyond Dawson.
And Pukki fired in a third, after Norwich ripped through the Owls rearguard, to leave home fans stunned.
Dawson's out-stretched leg stopped Onel Hernandez adding a fourth goal, but the goalkeeper was helpless to prevent substitute Dennis Srbeny from making it 4-0.
Dawson was having a busy afternoon, and quickly denied Hernandez and Srbeny as his defence crumbled in front of him.
Luhukay is deeply concerned about his side’s defensive frailties.
He said: “Everyone can see we are not consistent enough in our defending work.
“It was too easy, how we gave the goals away. You cannot win games when you give goals so easily away.
“We do not have the stability that we need. In the beginning of the game we had two or three good moments to score. It was a very, very disappointing game for us.
“I think we have the character - they did not give up - but when you don’t have 100 per cent confidence or trust, it’s not easy. We must fight to do better.”
Sheffield Wednesday’s next game is away at rivals Sheffield United on Friday.
Luhukay said: “We can only help ourselves and that is what we must try to do in the next few days.
“We do not have too much time to get back in a positive way. We are very frustrated and we are also angry.”