The Ghana international was on parade from start to finish as the Swans kicked off their 2020-21 campaign on a losing note.
A first-half brace from Tristan Abrahams in the seventh minute and on the stroke of half-time did the damage for Newport County on their home ground.
Following their disappointing exit on Saturday, manager Steve Cooper feels Swansea City were second best behind the League Two club.
"It's a disappointing result and a disappointing performance," Cooper said.
"Congratulations to Newport for going through to the next round.
"I think in simple terms, the non-negotiables of football, we were second best at today. When you do that, you always make it difficult for yourselves and that's what we did.
"We left it too late to try and get ourselves back in the game.
"No excuses. I know we're only a couple of weeks in, but we're not going to make any excuses, we were second best."
Ayew will shift his attention to Saturday's Championship outing when Swansea City travel to Preston North End for their league opening fixture.