Wednesday moved back into the Championship’s top-six after an own goal by Angus MacDonald and a late strike by Sam Hutchinson.
Carvalhal said: “We deserved to win. My players did absolutely fantastic.
“Barnsley are a very tough team to play against. They are very dangerous on the counter attack which is why they won 4-0 at Wolves and 3-0 at Birmingham. We gave the correct answer.”
He paid tribute to Hutchinson, who claimed his second goal of the campaign, saying: “All the team were good but Sam had a specific role to do.
“He’s a very clever player. It is why he plays in different positions. He understands the game. Not all the players understand the games. He knows what to do and was fantastic like all the players. We did very good team work.”
Carvalhal claims he missed Adam Hammill’s late sending off. The substitute was red carded following a collision with Hutchinson.
“I haven’t seen the image yet but I thought the red card was for Sam,” he said.
Barnsley boss Paul Heckingbottom and Owls coach Lee Bullen were both sent to the stands following the incident.
Heckingbottom said: “We are disappointed with the result. I thought we were good from the first to the last minute. I was pleased with how we played
“Wednesday deserved to win 2-0. They took their chances even though they didn’t have a chance in the first half.”
Heckingbottom was left baffled by Hammill’s dismissal: “I’ve not seen it back but my frustration is that I saw the ref give Sam the red card,” he said. “I knew Adam had been sent off but I didn’t know until I had got upstairs that Wednesday still had 11 men. I know I saw the ref give him a red card so I don’t know what happened.”