An early header from Carlton Morris deflected off Connor Ogilvie and into the net, while Cameron King added to the hosts' lead before the break.
Cristian Ceballos got us back in it with a fine strike from outside the area on 56 minutes, but a further goal from King put the match beyond us.
Norwich U21s: Rudd; Hall-Johnson, McFadden, Miquel; Toffolo; Bennett (C), Grant (Efete, 62), McGrandles, King (Ashley-Seal, 83); Hooper, Morris (Norman, 88). Substitutes (not used): Ramsay, Killip (GK).
Spurs U21s: McGee; Walker-Peters, Maghoma, Ogilvie, McQueen; Lameiras, Miller (Amos, 84); Sonupe (Pritchard, 75), Onomah, Ceballos; Akindayini (Georgiou, 79). Substitute (not used): Miles (GK).