Liverpool and Everton will face League One opposition in the Capital One Cup second round after being drawn against Notts County and Stevenage respectively.
The Reds, who won the competition in 2012, were one of 14 Premier League teams included in Thursday's draw. Manchester United, Manchester City, Chelsea, Arsenal, Tottenham, Swansea and Wigan Athletic will all enter the compeition at the third round because of their participation in Europe.
Newport County claimed a major scalp when they beat Championship side Brighton on Tuesday and the Welsh club, in their first season back in the Football League in 25 years, have been rewarded with a trip to Premier League West Brom.
Elsewhere, five-time winners Aston Villa -- only Liverpool have won the League Cup more times -- will host Rotherham, while West Ham face Cheltenham and Newcastle United travel to Morecambe.
Swansea are the Capital One Cup holders following their 4-0 victory in February over League Two Bradford, who have already been knocked out of this season's competiton.