City will wonder how they failed to win this game after missing at least four guilt-edged chances when leading 1-0 through Jordi Hiwula's 20th minute strike.
The visitors rode their luck and turned the game on its head, scoring twice after the break through Cauley Woodrow.
City Under-18s coach Adam Sadler told the club's website: "We knew Fulham would come at us after the break and they did exactly that, but we played some really good football in the first half.
"We had chances to increase our lead before half-time, but sometimes they just don't go in for you. We play Manchester United on Saturday and that will give us the perfect chance to bounce back. The lads are all disappointed but credit to Fulham who we wish well in the competition."