Ashby said the team will take some time tonight to celebrate their achievement in taking out the highly competitive challenger series, as well as reflect on how far they've come since San Francisco.
But he said the party won't go on too long.
"It's huge achievement for the team today, it's been a long journey to get to Bermuda," said Ashby.
"Hopefully Dalts [Grant Dalton]will give us half an hour to have a celebratory get together. As a group we're all very, very much looking forward to tonight, celebrating that tick in the box. We've ticked a couple and I don't think we'll be happy until we've ticked that final one."
Even since they arrived in Bermuda, Team NZ's journey has not been smooth.
They sustained damage on one of their first few days in the water, when, as they attempted the tight harbour exit got caught in a gust and nearly capsized. The net result of the incident was a day and a half of work in the shed for the shore crew.
A couple of weeks later the shore crew were staring a hole in the side of Team NZ's hull after a pre-start collision with British team Ben Ainslie Racing during a practice race.
But those setbacks all seemed relatively minor compared to the challenge the team faced after what Ashby terms Team NZ's "submarine exploration" last week. It was only six days ago the New Zealand boat - Aotearoa - returned to the dock a mangled wreck following a near-catastrophic capsize.
Peter Burling, who has shown incredible composure at the helm of Team NZ in his first America's Cup, said the team owe the new-look Louis Vuitton trophy to the heroes in the boatshed.
"The shore team has done an absolutely amazing job to get us out on the water and give us the tools we need to win. It was a great way to be able to repay them today."