The young Foxes, who are still searching for a first victory early on in 2020/21, kept Eagles goalkeeper Joe Whitworth on his toes throughout the early exchanges.
Terell and Kian Pennant, meanwhile, linked up well with the latter sending a low effort narrowly wide of the far post as City's youngsters looked for an opener.
However, with 38 minutes on the clock, Palace took the lead as in-form David Omilabu netted his sixth goal of the season with a composed finish beyond Arlo Doherty.
Leicester were unfortunate not to level matters after the break as Terell Pennant’s enticing delivery found Zak Booth, but his volley in the six-yard box was headed off the line.
As it was, the Eagles were able to hold out for a victory, as City turn their attentions to a visit to Brighton & Hove Albion on Saturday 31 October (11am GMT kick-off).
The details
City: Doherty; Wormleighton, Yfeko, Kutshitnza, Obi (Cook 41'); Madivadua (Butterfill 61'), Maswanhise, Cover, Booth, T. Pennant; K. Pennant.
Subs not used: Weeks, Stevens, Javid.