Despite having the much more experienced side at Championship level and being among the favourites for promotion this season, Wednesday found themselves 2-0 down after just 15 minutes at Hillsborough, leaving Carvalhal lamenting his side's defensive errors.
Speaking after the game, the Portuguese told 'Sky Sports': "It's a strange game for us. We never concede four goals, we never make these kind of mistakes.
"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.
"We need to be concentrated on the next games. The season has not finished, it is the beginning. We have done very well so far, it was a long time since we lost, and we must look to the future. The mistakes of my players are my mistakes, so I want them to be concentrated on the next games and have a strong reaction."
When pressed as to why his side made such uncharacteristic errors, Carvalhal concluded that the hostile atmosphere and early goal contributed to his side's downfall, saying: "Sometimes the emotional environment and going 1-0 behind in three minutes is not easy, the players get more nervous and we felt that.
"That's why we gave them chances to score and made mistakes we do not normally make. We reacted and came back into the game but when you take the third it's very difficult, and the fourth was very hard to react from.
"It was an important game but we have a marathon to run and we believe in our players and our team and we will react."