The under-fire Owls boss received plenty of criticism from supporters after switching from a 3-5-2 to 4-3-3 system in Saturday's defeat to top-six hopefuls Derby County.
The three-man backline helped provide Wednesday with a solid platform before the international break as they racked up their first Championship clean sheet at the 17th time of asking against arch rivals Sheffield United.
But Luhukay dropped Jordan Thorniley to the substitutes bench and selected a more attack-minded team against the ambitious Rams.
Yet again the Owls were the architects of their own downfall, with Derby capitalising on two pieces of poor defending to come-from-behind and inflict a fifth defeat in the last six outings on Luhukay's struggling outfit.
"When you look at the whole game, it had nothing to do with three, four or five at the back," Luhukay told The Star. "You must not make individual mistakes and that is why we are losing games in the period we are in.
"If you don't stop making the mistakes, you can't win games. It had nothing to do with three, four or five at the back.
"It's very frustrating when we look back on the last six or seven games and see how easy we give goals away. It is painful and frustrating.
"The players tried to do everything to come back into a good result in the second half.
"And then you must also have a little bit of luck also. The header from from Morgan Fox hit the post. If we were at the top of the league, the ball hits the post and goes in. Now it hits the post and goes out. That is the period we are in and it is frustrating."
Wednesday, without a victory in six matches, have fallen to 18th in the rankings, just three points above the relegation zone.
Luhukay said: "If we had beaten Derby, we would have had a situation where we would have come closer to mid-table.
"Because we lost, we know we have come closer to the teams at the bottom of the league.
"But that is reality and we must fight and not give up. I think the team did not give up against Derby. We must fight to get a little bit of luck and stop the individual mistakes."
The Owls face third-from-bottom Bolton on Tuesday aiming to secure a first Hillsborough win since August.
"We try to win every game," he said. "We will try everything to win against Bolton.
"Bolton will also be looking for the three points but we will try to bring the team back with confidence. We must have the trust with each other."
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