Hardcore Cyrus fans quickly took to social networking sites to vent after their favourite singer was relegated to No 2.
One told the Kiwi teenager: "Kill yourself you crusty old hag."
Another told her: "Your eyes are too far apart."
Cyrus quickly set herself apart from the criticism, contacting Lorde on Twitter and saying: "Why r people so mean? Ps your music is awesome."
Lorde, who grew up on Auckland's North Shore, has fast become an international hit.
This month she appeared on the cover of Billboard magazine, was praised by music legend Elton John at one of his concerts and had Royals covered by American pop sensation Selena Gomez.
Lorde also became the first woman in 17 years to top the US-based top alternative songs with Royals, which continues to reign.
Her debut album, Pure Heroine, is due to be released at the end of next month.