Wednesday suffered a chastening 4-0 defeat on their last trip to Ashton Gate back in March. Striker Bobby Reid bagged a hat-trick as the Robins tore the Owls' depleted team apart defensively.
Luhukay described the loss as "one of the most difficult" matches of his tenure.
When quizzed on where it went all wrong in the last meeting between the two clubs, the Dutchman told The Star: "I can't speak about that; t is in the past.
"We had no control over a lot of moments.
"At that time, Bristol had a very good team with good, dangerous strikers. Bobby Reid was there and he was their top-scorer. He was very successful against us. He went to the Premier League last summer.
"We had no stability. They changed a lot of positions at the time. They deserved the win.
"Now they have changed some of the players. They have new players. Jack Hunt joined them in the summer from us.
"The team find themselves in a good position in the league.
"The winner on Sunday can come closer to the play-off positions. It's a very important game for both teams."
Luhukay, who has confirmed Almen Abdi and Sam Winnall are pencilled in to play for the Under-23s next week following long spells on the sidelines, claims Wednesday are a "different team" from their last duel with the Robins.
"They have signed some players but their coach is the same," he said. "We have some changes in our team.
"Both teams are going in a positive direction. On Sunday, we will see two good teams play against each other. We must be 100 per cent mentally and physically strong."
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The Owls chief insists his team can take plenty of positives from the performance they produced in the Hillsborough draw against West Bromwich Albion last time out as they look to close the gap on the top six.
"We are very close to the top teams," he stressed. "If we had got the two points against WBA, we would be in the play-off positions.
"The distance to the play-off positions isn't very much. I think we deserve more points than we have, especially from the two home games against Hull City and West Brom.
"If we had four points more, our position in the league would be fantastic."
There is a strong possibility Luhukay will make changes to his team for their final outing before the second international break. Barry Bannan is in line to start in midfield, having served a one-match suspension, while Jordan Thorniley and Steven Fletcher are also pushing for first-team recalls.