The billionaire tech mogul had filed a legal case seeking to acquire small pockets of land within his large estate on the island of Kauai.
But his use of the so-called "quiet title" legal system led to criticism from other residents.
He said he had not taken the time to fully understand the process. "It's clear we made a mistake," he said.
Mr Zuckerberg bought a 700-acre estate on the Hawaiian island, where he says his family wish to "put down roots".
However, the estate is littered with a number of small parcels of land called kuleana.