The Tykes had two men sent off in the Hillsborough encounter, while Wednesday also had a player dismissed in a feisty local affair.
"The players were absolutely fantastic today," Wilson told the club's official website. "Given the circumstances during the game I thought they reacted brilliantly to it. They've put in a real real man performance, every man.
"When you see the fans standing up at the end and applauding them off the pitch, they know the commitment they have showed for them. The frustration comes with the lots and lots of decisions that everyone is questioning.
"Sheffield Wednesday will question decisions, we will question decisions, particularly when the board goes up with five minutes and the goal comes in the 96th or 97th minute. I just don't know where the time has come from. The lads were brilliant and they had a tough hand dealt to them today and they responded really well to it.
Following the defeat, Barnsley remain in the Championship's bottom three, five points from safety.