A shambolic opening 45 minutes saw City excel and be unlucky not to be 5-0 up at the break after hitting the bar twice and scoring three times.
Wednesday replied through Chris Eagles in a better second-half showing but realistically, it was the worst performance of the season.
Sturrock said: "I wanted the commitment from the players in the second half and we got that, but I'm so frustrated at our defending in the first half and to let a striker run straight through twice is terribly disappointing.
"Their strikers effectively bullied our two defenders and I do feel there is complacency among the players now with us having a lengthy injury list."
Frankie Simek got booked for petulantly throwing the ball away in the last few minutes and now he will face a suspension because he has accumulated five yellow cards.
But Lee Bullen, a ready-made replacement for the American may miss the Watford game after he pulled a hamstring during the warm down.