Carvalhal was left unhappy with the level of officiating in the East Midlands, however, having seen centre-back Glenn Loovens dismissed for a fourth-minute challenge on Matej Vydra, who picked himself up to net the resulting penalty.
To make matters worse for Wednesday, they had a big call go against them later in the match when Craig Forsyth shoved Steven Fletcher in the back, with Derby going on to net a second through Bradley Johnson late on.
Speaking after the match, Carvalhal said: "This is the fourth game in a row where we have critical decisions against us. [The Loovens incident] seemed like a penalty and a red card but when we have a similar situation, it makes a massive impact because it could be 1-1 and Derby will play with 10 players.
"I don't know if I'm more upset that the referee doesn't give the penalty or what he says to Fletcher because he says to Fletcher 'I saw that he push your shirt but you must stay up', which I think is bad in my opinion.
"But I know my players and after this game, with this performance and what we did by showing the heart and commitment, it makes me believe the future will be better."
Wednesday have back-to-back home games to come over the next nine days, as they welcome Barnsley and Millwall to Hillsborough.