"We don't normally have good games when there are milestones involved," former Aussie player Hager quipped.
He agreed defence would be his troops biggest work-on as they prepared for India.
"Defensively we were outclassed. We gave Korea too many opportunities, too many penalty corners.
"We can't afford to do that against the better teams."
Korea, who are ranked ninth on the world rankings, five places below the Kiwis, finished with 15 shots on goal, the same amount as their hosts. Black Sticks goalie Georgia Barnett produced a superb performance.
"It's very good to have both goalies playing well," Hager said, referring to the fact his other keeper Amelia Gibson was admirable in Sunday's win against Argentina.
Hager warned India would be tough.
"There are no weak teams at this tournament because women's hockey is so tight. Although they lost 4-2 to the United States the other day they played well.
"I don't think we are playing at our best yet. I imagine the statistics were probably pretty even for both teams, so I'm just really pleased we hung in there and converted enough chances to get us over the line," Hager said.
"As a team, one of the things we spoke about was having to win these close games, and we have won two in a row now. Both those games have been tight and hard fought, and we have come out on the right side."
Hager's troops allowed Korea to dominate the first quarter last night. The visitors finished that period with two penalty corners, while the Kiwis had none, and six shots on goal, five more than the Black Sticks.
However, the Black Sticks opened the scoring in the 17th minute when Olivia Merry scored from their first penalty corner. Far too often in the first half the Black Sticks' support players were too stationary on attack and they made hard work of clearing the ball from their red zone.
With Seunga Park impressing with her assists and workrate, Korea had the upper hand in the third quarter when they again finished 2-0 on the penalty corner count and 4-2 on the shots on goal.
After Flynn had her moment of glory in the fourth quarter of a game played in cold conditions there was no further scoring until Korea pegged one back with a 55th-minute field goal from Eunbi Cheon when the Kiwi defenders were a little too casual.
With Punt, Flynn and Barnett, defender Brooke Neal can be proud of her contribution.
In other games yesterday, defending champions Argentina beat Japan 2-1, China beat the United States 2-1 and Australia and India drew 0-all.
Tomorrow's other quarterfinals will see China take on Japan, Argentina meet Australia and the United States play Korea.
