The Blades were two goals ahead inside 15 minutes in the first meeting between the two sides in five years, only for the home team to battle back and level things up.
Despite the momentum being on their side, Wednesday failed to push on and it was United who would go on to bag another couple of goals in the remaining 25 minutes.
Carvalhal admits that the Owls made life extremely tough for themselves following their slow start, but he was happy with the character shown by his side to initially recover from two down.
"It's a strange game for us. We never concede four goals, we never make these kind of mistakes," he told Sky Sports News. "If you start losing the game 2-0 after 15 minutes in a derby it is very hard, but my players have a big heart so they came back.
"The third goal was a very hard moment, the way we conceded it, and the fourth... I must give congratulations to Sheffield United and say it is my responsibility. I want everybody to leave the players alone."
Wednesday, currently 10th in the Championship standings, return to action on Wednesday night with a trip to take on Birmingham City.