"This is in recognition of this unique situation and a market response that did not deliver to New Zealanders as it should have during a very cold winter evening," the power company posted to social media.
Meanwhile, WEL Networks said Transpower had "miscalculated" the load on its network which contributed to an "excessive load reduction requirement".
The Waikato-based energy and electricity provider said it "repeatedly" questioned Transpower regarding the volume of load it had instructed WEL Networks to drop, but said Transpower was "insistent on the volume".
WEL was asked to reduce its load by 20 per cent, what it claims was "well above the national average".
WEL chief executive Garth Dibley apologised for the power outage to some customers, but said they acted "in good faith with Transpower's instructions".
Genesis said it was working with the industry to make sure the power cuts don't happen again.
Consumer New Zealand head of research Jessica Wilson said under the Consumer Guarantees Act consumers should expect electricity that is reasonably reliable and safe.
Not getting power on one of the coldest nights of the year clearly failed that test, she said.
There were "strong grounds for compensation" and people should seek recompense for line charges they paid but did not benefit from.
Wilson said people should also be able to claim for what is known as consequential losses.
"So for example if your freezer lost power and you lost a lot of food, you'd be able to claim compensation for that as well."
Mercury said it would put $50 on the accounts of its affected customers.
Hamilton resident Anthony Billington, who lost power for an hour, said the money wasn't too important for him, but he did want better communication.
"I remember in the not-too-distant past, when lake levels were low you got a warning weeks in advance," he said, adding that his biggest frustration about Monday night was "the total lack of warning".
Energy Minister Megan Woods and Genesis Energy are to meet today to nut out what needs to change after the power outage.
Woods has blamed commercial decisions by power companies and pointed the finger at Genesis Energy, in particular, for failing to turn on its third generator despite having been warned there would be massive demand.
Genesis chief executive Mark England said the company had been made a scapegoat and he would be asking the minister why.
"To pick one company out of the crowd and single them out as the problem doesn't make sense," he said.
Woods said she was not scapegoating Genesis, but its generator at Huntly was the "critical piece that could have been turned on quickly".
- RNZ
