Karamoko Dembele created a goal for Luca Connell in the 34th minute but after Ewan Henderson was given two yellow cards early in the second half by referee David Dickenson the young hoops faced a tough task.
Tommy McIntyre’s side came close to going further ahead a couple of times but lost an equaliser to a deflected shot from Ciaran Dickson with five minutes left to play.
Each club plays each other twice before the final in April, last season Celtic won the trophy thanks to an extra-time goal from Robbie Deas against Graeme Murty’s starlets.
CELTIC: Mullen; Church, Hjelde, Deas, Paterson; Connell (Coffey 69), Robertson; Karamoko (Oko Flex 89), Henderson, Burt (Savoury 89); McGrath (Harper 60)
SUBS: Hughes, McKay, Murray