Dyer netted Swansea's second at the Liberty Stadium after Jordan Ayew had earlier put the Welsh side in front, but Dyer was quick to praise the impact of one of his teammates.
Abraham squandered a number of opportunities against the Championship outfit, but Dyer says that the Chelsea loanee was able to create space for the rest of the side with his running on and off the ball.
The 30-year-old told BBC Sport: "It was hard at their place so we knew it'd be tough. They're defensively strong so we had to get make runs in behind. It took a while but we managed to do it today.
"Tammy Abraham commits players and everyone else can exploit those spaces. He's been doing it all season and it's good to have a player like that, who also has a goal threat. He's a young boy with tons of ability.
"He should have put me in in the first half, I let him know about that, but he had the awareness to pick me out in the second. I got the low strike on target and thankfully it went in."
Swansea will now play either Rochdale or Tottenham Hotspur for a place in the semi-finals.