In the other semi-final, Japan lead Sweden 3-1.
Entering Thursday needing to overturn a 3-1 deficit, Britain lost the day's first race to fall even further behind.
All six crew members were safe. Full credit to the guys.
Ainslie battled back with a masterful victory in the second race to fend off elimination, but New Zealand seized the advantage at the start of the third and went on to a decisive win. And a huge thank you to everyone back home in Britain for supporting us.
"Ultimately we weren't able to catch up with the existing teams in time", sailing's most successful Olympian, who is not used to losing, added. Artemis chose to remain in the 34th America's Cup, although it missed much of the challenger trials in the 2 1/2 months it took to ready its new boat.
At the finish, skipper and wing trimmer Glenn Ashby and grinder Blair Tuke shook hands with the other three grinders.
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The Kiwi shore crew worked through the night to fix the damage to the platform and fairings, and put one wing together out of the pieces from the broken two.
"It's a similar situation with Formula One where they are looking for continuity and looking to try and bring more new teams in, reduce costs, so to have someone with Martin's experience in helping with those negotiations has been fantastic".
The mayhem came a day after Ainslie was forced to retire from two races because of serious damage to his wing sail.
It's been a dramatic week in the America's Cup challenger eliminations on Bermuda's Great Sound, and the main event is still a week away.
"I couldn't be prouder of the team today".
Sweden's Team Artemis completed its remarkable comeback to eliminate SoftBank Team Japan from the America's Cup Challenger semifinal series on Friday and set up a showdown with Emirates Team New Zealand. He also has a silver medal.
The last encounter of the day between the Swedish and Japanese teams was decided by a penalty call near the end of race, when Japan's skipper Dean Barker was judged not to have given Nathan Outteridge enough room around a mark.