Ben Earl, Alex Mitchell and Josh Bayliss scored England's tries, with Max Malins adding one conversion. Asafo Aumua got three of New Zealand's 10.
Scotland took fifth place with a 24-17 victory over Australia, sealed by a last-minute try from Charlie Shiel.
Wales beat Italy 25-24 to finish seventh, while Ireland beat hosts Georgia 24-18 for ninth.
England had beaten Wales, Samoa and Australia to top Pool A, before a 24-22 victory over South Africa booked their spot in the final.
New Zealand beat Scotland, Italy and Ireland to win Pool B, defeating France 39-26 in the semi-finals.
South Africa beat France 37-15 in the third-place play-off.
England suffered a heavy 64-17 defeat by New Zealand in the final of the World Under-20 Championship in Tbilisi.