Conor Coady was sent off in the 15th minute for a pull on Leon Clarke as he looked to be through on goal.
It was then the former Wolves man who broke the deadlock in the 39th minute as he converted a Enda Stevens cross.
Wolves had a chance to get back into the game as Diogo Jota was fouled in the box in the 50th minute.
Ruben Neves stepped up to take the penalty kick but saw his effort strike the outside of the Sheffield post and bounce wide.
Clarke sealed the three points for the home side to confirm Wolves’ second defeat of the season.
The Wolves boss admitted that the red card to Coady was the correct decision but praised his side’s character as they stayed in the game.
He began, “I’m disappointed, it’s a bad result. I thought we started well up until the moment of the red card.
“Even after that, we didn’t allow them too many things aside from possession but of course it is a bad result.
“We had a moment to get back in the game in the second half but the boys showed character - they only scored in the second half because of a mistake by us which we have to really look at and try to avoid.
“We have to pick ourselves up and show on Saturday that we want to fight for each moment and each ball.
“I think it is a sending off, the law is clear - if you are the last man holding an opponent when you’re not trying to play the ball, it’s a red card,” he said.
“In the second half we had a clear strategy and we went on to the pitch and controlled the game.
“Then there is the penalty, in that moment we were in control of the game even with one man less.
“It sounds absurd but I really think we were in control of the game at the start of the second half - we have the moment of the penalty and everything could change.
“Football is moments and when that happens, you have to look at them and try to avoid them - it’s a mistake, so lets try and correct that.
“We don’t waste too much time looking at that - the boys work well and show character, our fans can see that we were organised and we fight.
“The only way to do that is by working, working hard. It was a tough game, we knew that - Saturday is important for us to show that we want to go and fight until the end.
“We can win, we can draw, or we can lose but one thing you have to show is that we are a team and everybody works together.
“A mistake is our mistake - Wolves mistake and we answer that with the next game.
“Football gives you this chance after one defeat to go back again and make it better and that’s what we will aim to do.”
Wolves' next Sky Bet Championship fixture is against Burton Albion at the Pirelli Stadium on Saturday (3pm).