The Owls host Carlisle United tonight in a third round replay after being held to a goalless draw by the League Two outfit 11 days ago.
A home date with Reading or Stevenage awaits the winners, meaning there is a clear route to at least the last 16 if Wednesday can negotiate a safe passage past the Cumbrians.
Luhukay arrived in England last week as a promotion specialist after taking three clubs into the Bundesliga.
But the Dutchman also enjoyed a thrilling run in the DFB-Pokal, Germany’s main knockout competition, during his first season at the helm of FC Augsburg.
He led the second tier club to the semi-finals in a 2009-10 campaign that also brought a place in the play-offs.
“This will be my first home game but that is not important,” said the 54-year-old to The Yorkshire Post. “What is important is we get to the next round.
“Every game that you win gives you more confidence and maybe more trust in yourself and the team. Carlisle is an important game for us.
“I enjoy the Cups. One time in Germany with FC Augsburg, we did very well in the DFB-Pokal. We played at Werder Bremen (in the semi-finals). We had beaten two or three of the top Bundesliga clubs to get to that stage.
“It was not a happy day because we lost (2-0). But we were very close to the final. Of course, that happened in the past and we live in the future.
“We must look to the Carlisle game. But the Cup helped us in the league (at Augsburg) and gave us confidence and belief.”
Safe progress and a fourth round date on Friday January 26 – to avoid a clash with Sheffield United’s home tie against Preston North End the following day – would further boost confidence levels already lifted by Luhukay’s debut in the Championship.
A goalless draw across the Steel City at Bramall Lane was a heartening end to his first week at the helm, not least because the Owls had only 14 senior fit players available.
Glenn Loovens’s dismissal and none of the injured players Luhukay was without against the Blades nearing a return means his resources will be even more stretched against the Cumbrians.
Nevertheless, Wednesday are strong favourites to go through. “This will be a very different game to (last) Friday,” said Luhukay, who watched from the stand as his new charges were held at Brunton Park.
“I know a little about the opponent. Hopefully, we create chances and score goals. We had one or two chances to score (at Carlisle) but we forgot to score. We must convert our chances in the replay.”
Luhukay handed Sean Clare, fresh from a loan spell at Gillingham, a late debut from the bench at Sheffield United and he could turn to Connor O’Grady to shore up a defence without not only Loovens but also injured duo Tom Lees and Joost Van Aken.
Alternatively, the Owls may switch from the three-man backline that proved so effective against the Blades.
Either way, Luhukay admits the injury crisis that has left him without a depleted squad means Wednesday are having to keep a close eye on the transfer market.
“We now have a situation where we must have a lot of patience and maybe the injured players come back in the next weeks,” he said.
“But you know the transfer window is at the end of the month and we must look on what positions the injured players are maybe longer not there that we must do something.
“First, we must look to the Carlisle game.
“We play also on Saturday (at home to Cardiff City). We have to focus on the games and also on the squad, and what is happening with the players.”
Asked if he had provided the Owls hierarchy with a list of possible targets, Luhukay replied: “I speak with the chairman every day about the club, the team and players.
“We have very good conversations with each other. We are communicating every day over the players we have here, over the players who have injuries and maybe over new players.
“We have contact every day with each other. It is important that we always look at what we can and must do and at the end make a decision.
“As a coach or manager, you want to have every player in the training sessions.
“But now they are not there and I must try to give the players confidence. That is what is important right now.
“The players must have a good feeling and must try to win to get through to the next round.”
During Luhukay’s coaching career in Germany, those three promotions with Augsburg, Hertha Berlin and Borussia Monchengladbach were built on impressive home form.
“It is very important we make Hillsborough a tough place to come to,” he added. “When you win games, it always give you a better feeling.
“We always like to win. Every player knows that and you must not be afraid to lose in games. You play to win.”