"We're getting closer to putting together that really good match for the full 70 minutes," Couzins added.
While goalkeeper Devon Manchester along with attackers Blair Hilton and Hugo Inglis were the heroes in the penalty shootout - after the scores were locked 1-1 at the end of normal time - Couzins was one of those who could only stand and watch.
He was mortified to have a first-half penalty stroke hit an upright.
"Historically when we've had strokes I've been in quite a few of those," he said. "But I don't think I've been any more nervous than I was today. It is tough watching and a couple of our guys really responded to pressure moments, which is fantastic."
Inglis, who missed his chance in the shootout, then got one in the sudden death phase, then Hilton, despite being forced wide by Argentine goalkeeper Joaquin Berthold, slapped his reverse stick shot into the goal to seal the win, 4-3 on penalties.
Earlier Hilton and midfielder Steve Edwards scored shootout goals while man of the match Kane Russell, with a strong drag flick shot, had put the Black Sticks in front in the first half. Argentina equalised 12 minutes from the end after a scramble in the circle.
World No 1 Germany were beaten 2-1 by No 3-ranked Netherlands and Australia, ranked No 2, were 2-0 down to India before winning 7-2. They meet the Dutch in the other semifinal.
Even if New Zealand lose to England they are set to climb one place to sixth on world rankings. They could get to fifth at a pinch, by finishing third or better, and depending on other results.