A miserable week for Newport was compounded with a 3-0 loss at Salford who secured their first league win of the season.
The travelling Exiles, thrashed 8-0 by Southampton in midweek, continued where they left off in the EFL Cup and were behind after 38 seconds.
Gary Bowyer's side opened the scoring with Tyreik Wright lifting a delicate effort beyond the onrushing Joe Day.
The visitors conceded again shortly after with Conor McAleny finishing accurately into the far corner.
A spectacular Christopher Missilou effort cannoned off the post for Newport and, as Salford countered, Ian Henderson pounced on a slack back-pass before rounding Day and rolling the ball into an empty net.
Timmy Abraham thought he had gained his side a reprieve on the stroke of half-time but his effort was chalked off for handball.
Newport, without boss Michael Flynn after his positive Covid test, could have fallen further behind in the second half but Brandon Thomas-Asante's strike struck the post as the home side coasted to victory.