The 27-year-old winger found the back of the net just 82 seconds into the Swans' 3-0 win over York City in the second round of the domestic tournament on Tuesday night.
With competition for places high in Garry Monk's squad, Dyer has explained that he has been working hard in training to get himself in the starting XI.
"I've been working really hard throughout pre-season to get back into the first team," Dyer told Swans TV. "I have been working closely with [coach] James Beattie, so it was great to get in the scoresheet. I just want to prove I can get back to my best and push for a start."
Swansea are unbeaten after three Premier League games.