The Wednesday win was the Swans' sixth in succession on home soil in all competitions – their best run at the Liberty Stadium since 2007.
“I am very happy and very proud of my players," Carvalhal said.
“I was born in 1965. The club didn't do better than this in the cup since 1964, so it's been a long, long time.
“I am happy we have achieved this. Now we will play either Rochdale or Tottenham at home and we could go to Wembley, so we are in a very good position."
Carvalhal opened his blazer and pointed to some words embroidered on the inside pocket.
“I have 'Carlos had a dream' written here in my jacket," he explained.
“All of us have dreams – the people who don't have dreams are not happy people I think."