Swans reached their first quarter-final since 1964 with a 2-0 home victory over Wednesday.
Dyer raced on to Tammy Abraham's pass to slot his shot between the legs of Owls goalkeeper Cameron Dawson and ensure Swansea manager Carlos Carvalhal would taste victory against the club he left in December.
“We made five changes (to the team which started at Brighton) and also we had Andy and Andre who could not play," Carvalhal said.
“I think we managed the game very well – for example Ki played only 45 minutes.
“I think we will be completely ready and fresh to play against West Ham and also we have progressed in the cup, so I am very happy."