However Fulham staged a strong comeback after falling behind and goals from Smith, Pierre and an injury time penalty from Marcello Trotta ensured that Town would not progress to the next round.
Speaking of the defeat, Academy manager Sammy Morgn said: "We're disappointed. We started slowly and Fulham definitely had the first 20 minutes.
"But we then had three glorious chances to score, which probably cost us in the long run. Fulham are a decent side, a footballing side, but I felt we had a hold of the game at 1-0."
Town Side: Ranieri, Bennett, Dunbar, Hyam, Meekings, Eastman, Clark, Cawley, Wickham, Murray (Lavery 85), Carson.