Newly promoted League One side Bristol Rovers will provide a stern test for the young Eagles, as will Plymouth who finished just outside the play-off places in the third tier last season. Swindon finished sixth in League Two in 2021/22.
All group stage fixtures will see Palace as the away side.
The competition is contested by the 48 clubs in League One and League Two, but Category 1 Academies can also take part to gain valuable experience of senior football.
Palace’s group is in the southern section of the tournament, with the top two from each group progressing to the knockout stages.
Last season, Palace took on Sutton United, Portsmouth and Wimbledon – securing a sensational 2-0 victory against the latter through goals from Jesurun Rak-Sakyi and Rob Street.