The 55-year-old has overseen just one win in nine games, as the Owls slumped from the play-off zone to 17th in the Championship in just two months.
Owls fans chanted for the Dutchman to be sacked in the 4-2 loss at Blackburn Rovers and 2-2 home draw with Rotherham United.
A veteran of German football as a player and coach, Luhukay has struggled to deliver results in his first job in English football.
“I was in German football for 22 years but I have never had what has happened in the last two games,” said the former Borussia Monchengladbech and Hertha Berlin boss. “It is not nice and it is also not respectful.
“But I know how football works with the emotion and passion. The fans love the club so you must accept that (the abuse) and try to be calm.
“The positive side is I have had a lot of success in my career but not right now in this period and you see how the fans have reacted to that.
“I have never had this in 22 years. I have a lot of respect in Germany, where I have a good status, and the people were very positive from the outside to me.
“But in two months, I am now not the same manager? I am the same person as before, the same coach, but the results in football decide your situation. I never thought it would be so negative and so hard, the criticism the fans gave me or the team.”
Luhukay accepts only a string of positive results can save his job, and with Owls owner Dejphon Chansiri due back in England next week – after several weeks in Thailand – the pressure is on to halt the slump, starting with today’s trip to Swansea City.
“Everything always depends on results,” said Luhukay. “The results are not positive. I have been in football long enough to know that nobody can tell me today or tomorrow my future is with Sheffield Wednesday.
“Every manager, whether you are in England, Germany or somewhere else, needs results and that is the most important thing for a manager.”
Chansiri’s public target of Premier League football seems a distant target, and Luhukay admits the Owls are even struggling to challenge for a top-12 spot.
Aston Villa are the only team in the top half of the table Wednesday have beaten this season. Four of their six wins came against the Championship’s bottom four.
“This club has fans who love the club, have emotion and passion, and when the results are not there they have a high expectation from this team,” said Luhukay.
“I must handle that, but I am not unrealistic. I know what we are doing every day, and know what this team can do.
“In football, a lot of times, you have unrealistic expectations from people. When we look up the table, of the first 12 clubs, we have only won against Villa.
“That’s a fact that we are not strong enough for the play-off positions. We have a team who can not expect to be in the play-off positions. That’s the reality.”