The semi-final winners will go head-to-head to decide who gets to challenge holders Team USA for the America's Cup itself, starting on June 17.
Burling said the capsize "was fully our error" as the boat accelerated and got high on its foils. He said the crew would review video to see what precisely went wrong.
The New Zealand boat suffered serious damage as it capsized, leaving a question mark about whether they will even be able to fully fix the boat in time to get back out on the water.
The British crew had suffered equipment failure on Monday when part of their wing controls broke, meaning they had to forfeit two races to their New Zealand opponents.
One broken wingsail in warmups on Wednesday and a subsequent capsize that damaged the replacement sail and placed questions marks over structural strength and electronic and hydraulic functionality has the Kiwis on the back foot. He trails the Kiwis 3-1 in the best-of-9 series.
Bendigo's Glenn Ashby has made a strong start to the America's Cup semi-finals with Team New Zealand. It looked like a slight misjudgement of the rake and angle, but all of us here are not going to pass criticism, Ainslie said.
"I don't think in 30 years of sailing I've ever experienced anything quite like that", Ainslie said of racing the temperatmental AC catamarans in winds averaging upwards of 21 knots (38.89 Km/h) with gusts even higher. "These boats are incredibly hard to sail and these things can happen".
"Thank God, most importantly, everyone was safe and okay and I'm sure they will be back out tomorrow".
Japan took a 2-1 lead over Sweden when the struggling Artemis retired from their first race of the day. "We look forward to seeing them back on the race course", he added.
"It's definitely sailing on the edge", Japan's skipper Dean Barker told BT Sport after completing the race.
America's Cup Challenger Playoff : From June 4 to 12 (may end earlier), the top four Challengers split into two Semi-Finals (best of 9) with the victor of each match to meet in the Final (best of 9) to determine who will take on Defender in the America's Cup Match.