It was an abject display from the Owls, who were outplayed by their South Yorkshire rivals but earned a point they did not deserve through Lucas Joao's double.
That was not enough to appease their angry supporters, who demanded for the Dutchman to lose his job after just one win in their last nine games.
But Luhukay refused to engage after the match when asked if he feared for his job, saying: "I am not deaf. This question you can ask, but I will not give you an answer to this. I cannot give an answer to this."
The Owls somehow took a half-time lead with their only shot on target as Joao capitalised on a defensive mistake, but two goals in the first 11 minutes of the second half through Michael Smith and Richie Towell put the Millers ahead.
Joao's second nine minutes later earned Wednesday a point, but that did not save Luhukay from the full force of the Hillsborough crowd's frustrations.
"I think the draw at the end was the result for both teams," he added. "We scored the first goal at the right time, you thought it would give us confidence for the second half.
"This period is not easy for the team, they are expecting more, there is more pressure on my team than the opponent.
"They can win, but we must win and that is a different situation when you start the game. Rotherham are a team who are strong and fighting, it is not easy to play against them.
"In the second half the game turned in the first 10 minutes in a positive way, but we came back into the game and deserved the 2-2 draw.
"We have to go further in your work with the team and you hope that every new game you find your way. Next week we have a new chance."
It has now been 36 Championship away games since Rotherham came home with victory, but that horrible run should have ended here as Will Vaulks and Towell missed two gilt-edged chances to restore the lead.
Their inability to win a game they deserved to is symptomatic of their season, though, and they have now drawn nine of their last 12 league games and sit just above the relegation zone.
"I am biased, I thought we were the better team, the aggressive team, I thought we tried to win," boss Paul Warne said. "We tried to get at them and I thought our first-half performance to go in at 1-1 was harsh.
"We did well in the second half and created enough chances in the end to win the game, but regrettably we didn't.
"But to get a point away is not my worst day at the office.
"We don't take enough chances to give ourselves a two-goal cushion. Over the course of the play people might think a draw was a fair result.
"We need to turn these draws into wins. In this league we need to take our chances, our chances were gild-edged. If they were at the other end I think they would have gone in."