The Welsh side came from a goal down to score twice before the death in order to claim just their second win since mid-October.
Jordan Ayew’s finish from close-range cancelled out Andre Carrillo’s opening goal before Luciano Narsingh sealed all three points in the 90th minute on the rebound from Nathan Dyer’s effort.
Just the first step
Speaking to the gathered press after the game, Carvalhal said: “Before the game I said if you ask 100 people, 100 will say we will be relegated. In this moment, in 100, 98 will say we will be relegated. Maybe two people will look and say maybe not! It is still a small percentage, we are not in a good position, but confidence and belief is high. Me, my chairman, players and fans are not in the 100.
"We believe. It will be tough. This is just the first step.”
The new Swansea manager made several tactical changes, both ahead of kickoff and mid-game. He said: “We brought Luciano on to give more pace to the team and we started doing the things to try and win, they are moments where we are lucky, such as the ball that hit the post for us early because our strategy would be more effective, but also when Lukasz [Fabianski] made a fantastic save from Gray which was crucial. Because we then scored to make it 1-1.”
Fabianski made a vital save just minutes before Swansea equalised, as Andre Gray closed in on goal from close-range but the goalkeeper was equal to his effort.
“The commitment was very strong.” The 52-year-old said. “We tried to give this message to them. We changed the formation and it is not easy in two days to play fantasy football and do this. It wasn’t exactly what we wanted, because it is impossible in 2 days. But I am happy with what I saw, if this is the beginning, we will be better because with more training to change the dynamic we will be better.”
After getting off to a winning start, Carvalhal said: “Of course I am pleased. We finished the game trying everything, two attackers, two wingers, Sanches in the middle, Olsson playing like a winger. We tried to win. But regardless if players do not play with heart we do not have this victory. The fans were crucial for us.”
“We started the game with four midfielders,” Carvalhal explained as Renato Sanches and Sam Clucas were tried as wide-midfielders in a 4-4-2 shape, “tried to confuse Watford with wingers inside the pitch and attackers open, but we didn’t achieve exactly what we wanted. We felt some problems against their No.8 but we corrected it with Carroll more on the right, after that we started stabilising our game. We controlled Watford’s dynamic.”
Carvalhal continued: “It is not because we won game it will be flowers and birds, it will be very hard, we have a difficult game against Tottenham who have not played this weekend. Tomorrow they will rest and rest again and play on Tuesday so it will be difficult, but we will be ready.
“We will start to prepare for Tottenham on the bus and analyse them. In this moment I just know the general things.”
Swansea host Tottenham Hotspur on Tuesday at the Liberty Stadium, where his side could even move out of the relegation places if results go their way.