The Swansea boss left Wednesday in December, just four days before taking over from Paul Clement at the Liberty Stadium.
The FA Cup fifth-round tie ended in a 1-1, and Carvalhal admitted it was a tough game for him.
"I almost cried after the game when two fans came to talk with me," he said. "It's a very emotional moment.
"I must say thank you to Sheffield Wednesday for the way that the fans received me, the buzz in the stadium, the players, also the manager (Jos Luhukay), the staff, everybody.
"It's the part that I love in football. That's the beauty of football, football is very positive, it is something nice, it's not negative.
"Sheffield Wednesday fans are unbelievable. I know that a player or a manager who works hard, gives 100% to the club will be 100% sure to get recompense.
"I felt big recompense for everything I gave to Sheffield Wednesday and I'm very proud about this moment. It's something I'll never forget."