Ki Sung-yeung's 81st-minute strike gave the Swans their third consecutive home win in the league and extended their unbeaten run to nine matches.
Carvalhal, whose arrival at Swansea has led to the team's upturn in form, joked about putting "all the meat inside the grill" in terms of bringing on attack-minded players in order to secure victory.
"I am very happy with my players, very proud of them, they are doing fantastic work. They follow 100% the strategy we create, very professional," the Portuguese told reporters after the game.
"We blocked [Burnley], we started creating problems and as you know during the game I was not happy because we wanted to win, we felt we really wanted to win which is why as a manager I can start to risk and put more players in attack.
"We put in Andre Ayew, Tammy Abraham, we had three attackers in the middle. We put all the meat in the barbecue, all the meat inside the grill, because we wished to win the game. I am very happy because that created a big impact."
The result sees Swansea climb to 15th in the table, two points clear of the bottom three.