They'll also be without midfielder Ria Percival, who left the field in the 30th minute with a potentially serious knee injury.
"If we will look at us, the whole game and how we perform - that was just unbelievable, and we can't wait to face Australia again," said Klimkova.
"We've learned the lesson. You need to really keep fighting that way to the end. But again, it's an unbelievable journey from our team, how we bounced back after the She Believes tournament where we didn't perform how we wanted.
"We are very proud of our performance and we still have things that we need to really improve in the next game. [But] we will be prepared."
The match surely ended any doubt about Esson's status ahead of Erin Nayler, with the 31-year-old managing another superb display, with a series of vital saves.
"She kept us in the game many times," said Klimkova.
Defender Claudia Bunge was another standout, with probably her only lapse coming in the 94th minute, when Emily van Egmond was left free to shoot home from 12 yards.
The opportunity had come after Ali Riley charged forward to try to win a loose ball on halfway and Australia broke, with the left flank exposed.
The winning goal was a testament to Sam Kerr's predatory instincts, after New Zealand couldn't deal with a corner, though Kerr had gone close minutes before with a similar header.
Earlier Anna Green's spectacular goal from near the touchline was one for the highlight reels, regardless of her intention as she struck the ball.
"Anna scored a great goal," said Esson. "That's all that needs to be said about that."
Esson cut a disconsolate but proud figure afterwards, as she pondered what might have been.
"It's gut wrenching losing how we did but in saying that I'm really proud," said Esson. "At times we had to weather the storm and our defending in front of the box was phenomenal in the second half, bodies on the line. That's something we really stepped up with."
The Ferns are waiting on scans and assessment of Percival's condition.
"Hopefully, fingers crossed, we all believe that it's not going to be a long-term injury," said Klimkova. "So we'll see how it goes."