The Swans were held to a 1-1 draw in the first game at Meadow Lane but put in a superb performance to coast into the fifth round of the competition at the expense of the beleaguered Magpies.
Carvalhal played down the importance of the victory being Swansea's biggest winning margin in their FA Cup history, instead focusing on how his charges approached the tricky challenge.
"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," Carvalhal told BBC Sport after the game. "I [told] 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."
The result means that Carvalhal will be taking Swansea to his former club Sheffield Wednesday in the fifth round of the competition.