The Swans manager showed his gratitude to supporters, applauding the crowd after enduring a difficult time in recent weeks following the death of his father
The former Reading boss, who recently lost his father, applauded fans after the game, which the Swans won 3-0 to secure their first win of the season.
And the 38-year-old further showed his gratitude when talking to Sky Sports after the victory.
"Swansea is a very special club with special supporters," Rodgers said.
"They've given me everything since I've been here and I was just applauding them and giving them my token of thanks for all the support I've received in the last week or so, which has been phenomenal."
Leroy Lita, Scott Sinclair and Nathan Dyer were all on target as Swansea romped to victory, but Rodgers was also happy to see his side keep another clean sheet.
He added: "It's a hallmark of our game.
"People pick up on our style in which we play. But there's also a great steel about it. That's our third clean sheet in five games.
"Last year in the Championship we had 22 clean sheets in 46 games - in nearly half the games we didn't concede."