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.

Andreas Von Knorre and Elton Hinz pleaded guilty to entering a train depot and spraying graffiti on a train.
Singapore has strict laws on vandalism, and has caned and jailed foreigners in the past for the offence.
These include a Swiss national in 2010 and US teenager Michael Fay whose 1994 caning sparked global controversy.
Von Knorre, 22, and Hinz, 21, had flown into Singapore from Australia in November last year and vandalised a train during their stay.
They left the country afterwards and were eventually arrested in Kuala Lumpur in neighbouring Malaysia.
Both men expressed remorse in court, and called their acts "a stupid mistake".
Caning in Singapore involves being struck with a wooden stick on the back of the thigh, which can leave permanent scars.
The maximum penalty for vandalism is a fine of S$2,000 (Â£958: $1,461) or up to three years in jail, in addition to three to eight strokes of the cane.
In 2010, Swiss software consultant Oliver Fricker was jailed and caned for spray-painting graffiti on a train in Singapore.
American Michael Fay made international headlines when he was sentenced in 1994 for damaging cars and public property. Despite an appeal from US President Bill Clinton, Singapore authorities went ahead with the caning but gave Fay a reduced number of strokes.

The man was seriously injured when he was struck at Kentish Town station in north London on Wednesday.
Devindra Ferguson, of Colindale, north-west London, was arrested on suspicion of attempted murder on Thursday.
British Transport Police said the 28-year-old is due to appear in court later.
A spokesman for the force said the victim is "still in hospital in a serious but stable condition and will probably be in hospital for some time".
England suffered a heavy 64-17 defeat by New Zealand in the final of the World Under-20 Championship in Tbilisi.
[NEXT_CONCEPT]
Two German men have been sentenced to three strokes of a cane and nine months in jail in Singapore for vandalism and trespassing.
[NEXT_CONCEPT]
A man has been charged with attempted murder after a Tube passenger was allegedly pushed into the path of a London Underground train.