He came off the bench to score twice in stoppage time and earn a dramatic 5-4 win against Crystal Palace on Saturday.
"I am very happy here. It is difficult for me because of the language, I would like to speak well, but I need to continue to study," said Llorente.
He also admits to having struggled on his return from a knee injury.
"After my injury I lost my performance level, but I always kept working in training and the coach sees this," said the 31-year-old former Juventus forward.
"Now I'm very happy because these two goals are very important for me, for my confidence and now I feel very good and I feel like I have helped the team."
The victory against the Eagles was Swansea's first in the Premier League since the opening day of the season, a result which took off the bottom of the table and above relegation rivals Sunderland.
Manager Bob Bradley met the Spaniard after "twisted" headlines suggested Llorente was looking to leave the club in January.
The American said, "It's typical, it is headlines that get twisted and people try to make a story out of something that's not really accurate.
"Fernando and I had a really good discussion.
"After arriving at Swansea, coming with an injury, and then having a few knocks after he arrived, we agreed that he wasn't at the level that we both knew he could reach.
"We understood that he's an important guy for the team and we had to move things forward the right way.
"The conversation that we had was so professional and neither one of us got bent out of shape by the way it was twisted in the press.
"We just said and agreed that we'll keep working together in the right way and against Crystal Palace he came on the field and made a difference for our team and it just shows you that he's a good man."
The Swans are 19th, two points adrift of moving out of the relegation zone and face three of the four teams around them in the table next month with Llorente hoping Saturday's win can transform them.
"What has happened is very important for me and for the team," he said.
"The situation in the table is close. This is now the time for change.
"After this I think the team have grown up a lot and this team need confidence."
Striker Fernando Llorente insists he is very happy at Swansea City despite being linked with a return to Italy within four months of joining them.