Dyer was an outstanding performer and Rodgers praised him and fellow wideman and goalscorer Routledge, whose strike was his first both for Swansea and in the top-flight.
"Tactically, Dyer was very good on the first goal," Rodgers said.
"People will look at his finish and run, but he read it very well, forced the mistake and then it was a great finish.
"It was good for both wingers. That was Wayne Routledge's first goal (for Swansea), which is incredible given the boy's talent.
"The first part of his move was terrific, great skill, and after it hits the post and comes back there is no time to think, but he shows great technique to finish in the bottom corner."