Former Australian star Hager conceded New Zealand had been outplayed for the whole game.
''We were too apprehensive and standoffish (early) and we didn't recover from that," he said.
''The disappointing thing for me is Kayla led so well but not enough players followed."
Hager said his players need to ''look within and ask themselves did they prepare properly".
He contrasted New Zealand's timidity in the 50-50 situations with the British players' do or die philosophy in the tackle and when making strong defensive plays, as exemplified by Britain's captain Kate Walsh playing with a broken jaw, sustained earlier in the tournament.
''When I saw Walsh diving in defence with a broken jaw, to me that said she wanted it and we didn't have people prepared to get on their guts and dive and win the 50-50 ball," Hager said.
''We thought it was going to happen because we had a good tournament and a good game against the Dutch (in their semifinal). So close yet so far. Because of the way we had been playing we thought it would continue on, but they were just more desperate."
New Zealand's only goal came too late to affect the outcome, midfielder Stacey Michelsen turning in a drive from Clarissa Eshuis at a penalty corner with just seven minutes left.
By then goals from Alex Danson, Crista Cullen and Sarah Thomas had made sure of the win.
New Zealand were sloppy on the ball, their passing and trapping below par for much of the first half. Britain took the initiative and didn't let it go.
The New Zealand players were clearly shaken as they left the arena by their failure to stand tall and seize the moment when an Olympic medal was on the line.
The British worked hard but were not overloaded with star performers. However, as Hager put it, they wanted it more.
''The most disappointing thing is we did exactly what we talked about not doing, letting the crowd and atmosphere get on top of us," striker Katie Glynn said.
''When you start on the back foot like that it's hard to pull yourself out. It's disappointing to feel like you let yourself down in the last game."
It is still the best Olympic finish by a New Zealand women's team, surpassing the sixth placings from Los Angeles (1984), Sydney (2000) and Athens (2004).