Half the 7375 dogs impounded in Auckland were destroyed in 2013-14 after being unclaimed by their owners and deemed unsuitable for adoption.
Only 508 dogs from the city's shelters were found new permanent homes.
"The 3016 dogs euthanised is way too high," said dog welfare advocate and Auckland Council member Dr Cathy Casey, commenting on the council's animal management report.
She said 151 or 5 per cent of the dogs put down could and should have been found new homes.
"Auckland Council must do better - every single adoptable dog must be given a second chance."
However, she added that council animal management officers and shelter staff had worked tirelessly.
One of the gains made since the merging of the old councils was establishing a single adoption website for dogs in the shelters. It has a photo and description of each dog and attracts 20,000 views a month.
The report said 75 per cent of the dogs destroyed were considered unsuitable for adoption because they were of a menacing breed, such as a pit bull. The rest failed a temperament test and a health check.
Dr Casey said the SPCA also had to put down a number of unwanted dogs not suitable for adoption. "It's clear the answer lies in getting your dog desexed as soon as possible."
She said the SPCA had a mobile clinic for free operations on dogs when owners could not afford the $100-plus vet fee, and the council offered a reduced registration fee for desexed dogs.
The report said 101,282, or 97.4 per cent, of known dogs were registered during the year and of 4843 infringement notices, 3203 were for failure to register a dog.