The auto park, which sits opposite the Echo Arena, became engulfed in flames after a fire in a Land Rover spread throughout all floors of the building.
Liverpool International Horse Show held at the Arena was cancelled and hundreds of spectators left without their vehicles had to use public transport to get home.
The fire was accidental but questions have been raised over whether a sprinkler system would have extinguished, or at least slowed-down the impact of the fire.
An insurance trade body says some £20 million could be paid out to victims of a Liverpool auto park inferno that incinerated some 1,600 vehicles.
In a statement issued on New Year's Day, the Echo Arena team said: "We are continuing to work with the emergency services who have worked tirelessly throughout the night to bring the fire under control".
The ABI said payments had already been made to some customers for vehicles and belongings lost in the fire.
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Nina Barbour, president of Liverpool Horse Show, said: "I would like to express my huge thanks and gratitude to the emergency services, the Echo Arena staff, riders, grooms and support staff, the general public and the City of Liverpool following Sunday night's events".
Liverpool Mayor Joe Anderson said the blaze started in a four-wheel drive vehicle on the third level.
Witness Sue Wright, who helped move some of the horses, said flames were shooting out of the Land Rover engine. Despite the damage, an arena spokesperson confirmed all people and horses are safe and that "there were no injuries during this awful incident".
"It looked like a ball of fire on the front of the vehicle and it was producing a lot of smoke", she said.
Merseyside Fire and Rescue Service/PA Temperates reached 1,000C during the blaze.
Residents living in apartments nearby and tourists staying in hotels were also forced to leave as 12 fire engines and aerial ladders were scrambled to the scene at about 4.40pm on New Year's Eve.