But his opposite number Lee Johnson blamed a huge mistake by the officials for Wednesday leapfrogging his Bristol City team into the Championship play-off zone.
Johnson was still raging after the game about Lucas Joao’s opening goal in the 64th minute, which he claimed was yards offside.
Substitute Joao netted again with a rasping drive two minutes later and, despite a late Matty Taylor penalty, smashed home after a foul by Josh Onomah on Callum O’Dowda, Wednesday held on to leap to sixth place.
Luhukay said: “I was not happy with what I saw in the first half. Bristol created several chances, while we had only one or two good moments.
“The second half was much better. We caused them problems, scored two good goals, and after giving away a stupid penalty defended really well at the end.
“Lucas Joao was having a difficult game after going on as substitute, not always keeping the ball. But he was different after his first goal and in the end was very important to us.
“If he wants to be in the starting line-up he has to work very hard in training day after day. It’s as simple as that.
“Josh Onomah was too aggressive in giving away the penalty, but I was pleased with the way we defended our lead at the end.
“Steven Fletcher hurt his back and Barry Bannan also picked up an injury. We have had an intensive period and I am happy about the international break.”
Johnson said: “I have watched the first goal again and it was three yards offside. We knew that at the time and it is so frustrating.
“The first goal in Championship games is so important and we have conceded it through sub-standard officiating. Every day we work with our defenders on squeezing up to get our high press going. An individual has let us down and it wasn’t one of my players.
“I don’t normally talk about officials, but it was such a key moment. I think they knew immediately that an error had been made.”
Bristol City: Maenpaa, Hunt, Webster, Baker, Kelly (Watkins 69), Dasilva, Brownhill, Pack, Paterson (Weimann 69), Taylor, Diedhiou (O’Dowda 69). Unused substitutes: Walsh, Hegeler, Eliasson, O’Leary.
Sheffield Wednesday: Dawson, Lees, Hector, Pudil, Palmer, Onomah, Bannan (Pelupessy 80), Thorniley (Forestieri 58), Reach, Fletcher (Lucas Joao 18),Penney Unused substitutes: Baker, Wildsmith, Kirby.
Referee: A Davies (Hampshire).