Lincoln City’s 3-0 win over Rotherham United ensured Rovers advanced from Northern Group H on goals scored, along with group winners Manchester United U21s.
Darren Moore’s side entered the evening needing Lincoln to win on the night but by fewer than four clear goals.
A third goal for the Imps on 87 minutes had nerves jangling for Rovers but Lincoln could not find the goal they needed to advance.
The result meant Rovers, Rotherham and Lincoln all finished on three points in the group.
The second round draw will take place at 2pm on Saturday with the games due to be played on the week commencing December 2.
Rovers will be drawn against one of the eight winners of the northern groups – except Manchester United U21s.
The other northern group winners were Leicester City U21, Accrington Stanley, Salford City, Port Vale, Everton U21, Manchester City U21 and Blackpool.