The Owls took the lead in the first half through Adam Reach but could not hold on to the lead as Harvey Barnes equalised in spectacular style.
The home side started the Sky Bet Championship game as the better side but their former goalkeeper Adam Davies was in fantastic form all afternoon, making several top-class saves.
However, Davies was powerless for the Wednesday opener, as Reach's 34th-minute shot deflected up and looped into the goal.
The visiting side looked determined to end their miserable run of results at Hillsborough though and Barnes hit a wonderful 67th-minute effort from the edge of the area that curled into the far right corner of the net.
Carvalhal said: "I think the highlights will show the history of this game. If you see the highlights, I believe it will show a lot of chances from our part.
"We had more threats, we played near the goal of Barnsley. Before we scored our first goal, we had three or four chances to score, even in the first 15 minutes.
"The opponents played with organisation, of course, they scored one goal. But they scored one goal from two, three situations they were near our goal.
"We fight, we run, we play with a big commitment, with big hearts, we create chances and we didn't give too many chances to the opponent to score. They scored one goal and credit to them, we didn't make a mistake."