The space agency was charged with finding 90 per cent of the potentially deadly rocks hurtling through space by 2020.
However, Nasa has not received the funding needed to build the necessary telescopes, according to the report by the National Academy of Sciences.
Nasa estimates there are around 20,000 asteroids and comets in our solar system - each exceeding 460ft in diameter - which are potential threats.
So far, scientists have found 6,000 of these objects using the current telescope system.
Disaster movies like Armageddon and near misses in previous years may have scared people and alerted them to the threat. But when it comes to monitoring, the academy concluded 'there has been relatively little effort by the US government'.
Rocks between 460ft and 3,280ft in diameter can devastate an entire region, said Lindley Johnson, Nasa's manager of the near-Earth objects programme.
It is widely believed that an asteroid, possibly measuring 13,200ft, wiped out the dinosaurs 65million years ago.
Nasa calculated that to spot the asteroids as required by law would mean spending about £480million between now and 2020, either with a new ground-based telescope or a space observation system, Mr Johnson said.