"We've been in this situation before, still a long way to go", Ashby warned after Team New Zealand won Sunday's two races over their arch-rival.
In the meantime, two more races are scheduled for Sunday.
The US team have spent the week working on making improvements to their 50-foot foiling catamaran in an effort to match the superior speed of their rivals, who are using a revolutionary cycling system with which their sailors provide the power needed to control the boat.
Spithill has been here before.
We came out of a good battle today and managed to take another win but we feel we have plenty more to come, Burling said. Before the racing began on Saturday, Oracle skipper Jimmy Spithill said they'd indeed made significant alterations in the set-up of the boat.
"We're frustrated with race one", Spithill said.
Spithill said the powerhouse American-flagged crew - backed by technology from Oracle Corp. and Airbus - continues to make too many mistakes. "They sailed very clean, very smart and they deserved to win two races".
Team NZ and all of New Zealand, should stay humble here.
"The boat is clearly faster because of the changes and it showed in the second race that if we as athletes can do a good job then the boat responds".
"We'll just come back out tomorrow, really take all the lessons from today and we'll focus on one race at a time".
"You've got to take your hats off to those guys today".
Its no secret that when you look at our team, we are all very young and the advantage that gives us is that we are all pretty open and learn fast..
"These guys sailed better".
After five days with no racing, both crews have been working to improve the performance of their space-age catamarans, with the pressure on the U.S. crew and their extensive design and technical team to pull something out of the hat. Although Spithill kept clear, the Umpires assessed a penalty - the second of the match against the American defender - and after ORACLE TEAM USA paid off the distance penalty, the Kiwis had sped off to a winning margin to take a 4-0 lead in the series.
But Team USA have made mistakes, which Spithill acknowledged.
At the start of Race 8, Burling wheeled underneath and then alongside Oracle, forcing the US boat to slow.
Oracle skipper Jimmy Spithill was put on the spot by 1 NEWS sports reporter Abby Wilson as his crew faced the prospect of losing the America's Cup to Emirates Team New Zealand.