The Swans are currently in the middle of a relegation fight in the league, but Carvalhal was buoyed by their positive attitude on Tuesday night.
Carvalhal said: "It is important if it is the best result in the history, but the most important thing is the attitude of the players that made all the difference. I spoke to them before the game that we have a challenge tonight.
"I am very proud of the players as they accepted the challenge. They made Notts County look like they are not a good team, but they are a good team. But we the way we played made the difference, the attitude was fantastic.
"We also finished the game with three boys from the academy and we never know if we will need them during the season."