The Eagles took the game to extra time late on when Sullay Kaikai levelled the game up at 2-2, but Paul Dummett won the contest for the visitors at Selhurst Park with a goal eight minutes from the end.
"I thought the youngsters deserved their opportunity and they didn't let us down," the Daily Star quotes Warnock as saying. "I had to look at a few players tonight. We can hold our heads up high."
Palace return to Premier League action this weekend when they host Leicester City.