''We were playing with 10 players for one quarter basically."
Young attacker Kelsey Smith had been sin binned for five minutes right at the end of the third quarter and for a time New Zealand had two players side by side cooling on the bench.
Hager confirmed the umpires sent the wrong player off for the second yellow card.
''They got it wrong by a mile. We were trying to tell them you've got the wrong person but they wouldn't change it."
There were also green cards for Anita McLaren and Petrea Webster in the first half.
That said, Hager admitted New Zealand had failed to take half chances and Australia took theirs to leave the fourth-ranked Black Sticks rooted to the foot of the table, after their 6-2 loss to world No 1 the Netherlands on Sunday.
Emily Smith put Australia in front in the third minute, after goalkeeper Sally Rutherford partially blocked the shot but the ball ballooned up and back over the keeper into the goal.
New Zealand equalised within a minute from Anita McLaren's crisply-struck drag flick from a penalty corner.
Australia regained the lead early in the second corner with a fine penalty corner strike, low past Rutherford's right leg, by experienced Jodie Kenny.
When Grace Stewart ended a quick counter attack by beating Rutherford at the second attempt shortly before three-quarter time it was all uphill for New Zealand.
In other results today, the Dutch beat Britain 2-0 and Argentina beat the United States 4-1, results which leave the New Zealanders rooted to the foot of the table.
New Zealand play Britain in their third game early on Wednesday.
