Papa John's Trophy holders Sunderland topped their group to earn a home second round tie despite losing to Bradford City on penalties.
The game went to spot kicks as it ended 1-1 at the Stadium of Light after Theo Robinson and Nathan Broadhead scored.
Gareth Evans scored the winner as the Bantams won the shoot-out 4-2.
Portsmouth, the 2019 winners, squeezed through thanks to George Hirst's last-minute goal in a 3-0 victory over Crystal Palace's Under-21 side.
Rotherham, Bolton, Aston Villa U21, MK Dons, Charlton and Leyton Orient were among the teams to have already qualified prior to Tuesday's fixtures.