Fernando Llorente saluted the travelling Swansea support after their shock 3-2 win in a "crazy match" at Liverpool on Saturday.
Llorente - who continues to be linked with a January transfer window move to Chelsea - said the team were inspired by the City support in a thrilling game.
"It was a great feeling to celebrate in front of our supporters and I want to say thank you to them," Llorente told the club's website.
"They come to support us everywhere and they are very important to us.
"I am happy because the supporters at Swansea are always behind us. When they sing my name as well, I can only say thank you.
"It is important that we have feeling when we are on the pitch and they are in the stand. We are all together."
Swansea blew a 2-0 lead, allowing Liverpool to pull back to 2-2, but Gylfi Sigurdsson scored the winner 16 minutes from time to silence the Kop.
"It was a crazy match," Llorente added. "I am very happy to win at one of the biggest clubs in the league. Liverpool are an amazing team with a great stadium.
"They are one of the best teams in the Premier League and to win makes us all very happy - it's an amazing result. Now we have to continue to work and try to move up the league table.
"We have to play always like we did today. We have demonstrated that we can play a good match, now we have to carry on like this."