The Swans won Carvalhal's first Premier League game in charge with a dramatic late comeback at Watford on Saturday.
The Portuguese only lost his job at Championship Sheffield Wednesday on Christmas Eve, but four days later found himself in the Premier League.
It was his second goal in three games and it proved vital as Swansea finished the year with three valuable points as they continue their fight for survival.
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"Everybody understands Swansea is in a very hard situation and a lot of people would say we need a miracle to stay in the Premier League". But confidence is more high, belief is more high.
"Me, my players, the chairman and fans do not belong to this 100".
From there, the Brazilian shot to the near post where Lukasz Fabianski parried the ball back into the area where Carrillo was weighting to nod the ball into the net for his first goal for the club.
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Watford then dominated proceedings and had a Molla Wague goal harshly ruled out for a slight shove on Tammy Abraham.
"Before the game I said if you ask 100 people, 100 will say we will be relegated".
"We created chances to score and we had a big chance moments earlier". We believe we can stay [in the Premier League] but it will be tough, very tough work.
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Silva said: "I didn't see much of a foul there. But I don't want to make excuses, we should have killed the match".