The Baggies bounced back from going two goals down to score twice in the last five minutes at Hillsborough.
Adam Reach and Fernando Forestieri scored in the first half before Barnes challenged Joey Pelupessy for Chris Brunt’s low cross with five minutes to go, with the Wednesday player appearing to get the decisive touch before the ball crossed the line.
Barnes then finished off a mazy run with a low finish with three minutes to go.
He said: “Of course you do not have a great feeling after the game. You must analyse what has happened in those two minutes.
“We played a very good game, we played good football and created chances and scored goals. It was a great goal from Adam and the second goal was very important when it came.”
After successive draws against Leeds and West Brom, he added: “We must think in a positive way. We played two top teams and we did not lose.”