Few pundits have backed the Owls, who kick off their Championship campaign on Saturday at Wigan Athletic, to figure in the promotion race.
Although their long-term injuries have cleared up, Wednesday have not brought in any reinforcements.
Luhukay told The Star: "We will try to do better (than last term's 15th place), of course. We must try to surprise people in the new season. Let's see where we come."
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The Dutchman, who has refused to rule out more players leaving Hillsborough before the summer transfer window closes on August 9, is feeling positive about the 2018/19 season.
"What I see in training every day gives me belief that we can find a good direction in the new season," said Luhukay. "Hopefully we can make a good start, which leads to more confidence.
"We will look forwards and upwards and think positively."
The Owls' players put the smiles back on the fans' faces with their strong end to last term. A run of six victories from their last nine fixtures lifted them up to 15th.
"The last two and a half months last season were fantastic," said Luhukay. "The results were very positive and we must make it that way when we start the season.
"I think the injured players being back make us stronger than last season. Sam Hutchinson is back, Joost van Aken, Steven Fletcher, for example, Barry Bannan. They have no problem with injuries in the last five weeks and all of these players have their own qualities, so they make the team better.
"I hope we can make the fans enjoy what they see."