Saturday’s draw with South Yorkshire neighbours Barnsley means the Owls remain in 17th position, just six points above the relegation zone.
But Wednesday, who had 14 first-team players unavailable for selection through injury and suspension, could have snatched maximum points at Oakwell. Both Ross Wallace and Joey Pelupessy went close to grabbing the winner in the second half.
Luhukay, still searching for his first Championship victory as Wednesday boss, told The Star: “We must score more goals. We had the chances (against Barnsley). We had five or six opportunities where we could have scored and we must work on that.”
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While the Owls posed more of a threat as an attacking unit after the break, Barnsley edged the first half and Joe Wildsmith produced two superb saves to deny Tom Bradshaw. Academy starlet Wildsmith also kept out Reds loanee Oli McBurnie after the interval.
Luhukay said: “Both teams had chances. At the end, we must live with the draw.
“Joe was very good in goal. He made three or four fantastic reflex saves.”
McBurnie’s fine individual goal cancelled out Atdhe Nuhiu’s 18th minute penalty after Barnsley skipped Andy Yiadom was penalised for bringing down Lucas Joao.
“It (the goal) was very important for Atdhe’s confidence,” said Luhukay. “He has been in good shape in the last few weeks. We are happy with him.”
Luhukay has been forced to turn to youth due to Wednesday’s mounting injury list. Frederik Nielsen and Jack Stobbs were second half replacements and midfielder Connor Kirby was included for the first time in the matchday squad.
He said: “We have a very small team so we had three or four players from the Under-23s.
“We have a difficult situation but we think positive.”
Daniel Pudil could feature against Derby County on Tuesday night, having completed a one-match suspension.