After a slow start Jerry Gill's Canaries imposed themselves on the match but failed to convert a number of opportunities.
They were punished as Fulham went into a two-goal lead, but City's reaction was positive and they pulled one back before half-time.
Swift combinations in midfield allowed Louis Ramsey to cross for Todd Cantwell, with the England Under-17 international finishing well.
The second half followed a similar pattern, but even though Norwich failed to capitalise on further opportunities, they can take heart from a performance of high quality.
NORWICH CITY: Oxborough; Ramsey, Lewis, Grant, Efete, Fox, Byrne-Hewitt (Walters 74), Black (Couzens 62), Ashley-Seal (Simpson 77), Cantwell, Eaton-Collins. Subs not used: Beauchamp (GK).