Dyer's pace helped open up the Bolton defence and aided goals from Joe Allen, Scott Sinclair and Danny Graham.
"Our mentality is to create and be on the front foot. It was one where we really got after them, our wingers are a threat," Rodgers said.
"We open up the pitch, get good width and our game is to get the ball into wide areas and we know when we get there we have the players to make a difference.
"I thought Nathan was brilliant at that. He gets after people. They felt that was a threat because Robinson didn't start, they put in Gardner who is quick."
Swansea are currently 10th in the Premier League with 12 points from 10 games.