The Team GB pair finished seventh in the final with just 382.80 points as China took the gold ahead of the USA and Germany.
Laugher won in Rio five years ago with Chris Mears, but the reigning champion and Goodfellow were uncharacteristically never in contention in Tokyo.
The pair were last after the opening round of dives with 47.40 points and never recovered.
An inward three-and-a-half somersault tuck in the third round scored them just 63.24 after Goodfellow, who won synchronised 10m platform bronze with Tom Daley five years ago, over-rotated on entry
Another poor fourth-round dive kept the pair last and a forward four-and-a-half somersaults effort in the fifth earned just 62.70 points.
Their final dive, a forward two-and-a-half somersaults three twists pike, was comfortably their best and at least lifted them off the bottom of the standings.
Laugher and Goodfellow avoided finishing last after the Russian Olympic Committee team’s final effort was ruled as a no dive.
Elsewhere, Tom Dean became the first British male swimmer to win more than one gold medal at a single Olympics in 113 years after helping his nation to victory in the 4x200 metres freestyle relay final at the Tokyo Aquatics Centre.
Dean produced the performance of his life to triumph in the men’s 200m freestyle 24 hours earlier in a British record time, and he made a solid, if unspectacular, start in the relay race before his team-mates finished the job.
Alongside Dean was Duncan Scott, who claimed silver in Tuesday’s individual race, James Guy and Matthew Richards, and their time of six minutes and 58.58 seconds saw them bag Team GB’s third swimming gold of Tokyo 2020.
Dean is therefore the only British male swimmer to claim two golds at the same Games in more than a century, following in the footsteps of Henry Taylor, who prevailed in the men’s freestyle 400m and 1500m races in 1908.