The visitors were the dominant side for much of the first hour of a dour south Yorkshire relegation scrap, but they paid the price for failing to convert their chances.
Gary Madine and Reda Johnson gave the Owls a two-goal cushion, and an added-time strike from Jacob Mellis was little more than a consolation.
"We have got to be constructive, the two goals were disappointing, they came when we had momentum," he said. "When you have a foothold you have to make sure you lock that down.
"The second goal has really disappointed me, we had to be brave. At 2-0, the momentum is with Sheffield Wednesday and I didn't want it to turn into a rout. To come here and leave with a 2-1 is the only positive we'll take.
"I have picked these players up before. They are eight more games to look forward to.
"The pressure on us is to stay in the league, but the pressure is on other teams to get out of it and they are just panicking and we have to take advantage.
"The players are hurting but when we leave here, we leave proud and in a positive state of mind."