The first half of the game was lacklustre from both sides, with chances in the opening 45 minutes few and far between.
The home side were winless at their Hillsborough stadium in seven games beforehand, with a 2-1 defeat at the hands of Derby County on Saturday.
Bolton, meanwhile, have now seen their winless run extended to nine games in the league, with the Trotters netting just twice in that period.
Wednesday captain Tom Lees (57) got the only goal of the game, heading home a Barry Bannan corner and while the deficit gave Bolton a short burst of energy, they could not breach what was a tight home defence.
The home side could even have added to their lead late on, with good chances falling to Adam Reach, Lucas Joao and Fernando Forestieri, which they failed to take,
Luhukay said: “I think the team is very happy now. I think in the first half, we find not the way in the game and the players were very nervous. They make a lot of mistakes when we had the ball.
“We find not the good combinations to come to good chances or to scoring a goal. I think the pressure was high today and you see it in the first half on a lot of players in my team.
“But in the second half we started good. In the first ten minutes we make good goal a set piece from Tom Lees and I think in the second half we had a little bit more of the ball and we came to some chances.
“You see today you have not so much clear chances, but one goal today was enough to win.”