Jonny May scored a brilliant solo try and Owen Farrell landed three penalties but the visitors stayed in contention through a try and two penalties from fly-half Aaron Cruden.
Tries from captain Richie McCaw and replacement Charlie Faumuina capped a dominant second-half display, despite a late converted penalty try from Stuart Lancaster's side.
Yet Hansen believes it was a critical period in which England failed to exploit their man advantage after hooker Dane Coles was binned that proved the difference.
"If your team has more caps than the other and you lose they tell you they are too old and should retire - it's just an excuse," said Hansen.
"In that first half England were probably half a click in front of us the whole time, showed a bit more desperation and urgency to get to places.
"We talked about it in the changing room at half-time - we needed to get urgent before we needed to get desperate in the last five minutes.
"The reality is we won the game in that ten minutes because we were able to play with 14 men after Dane Coles reacted to being pulled off his feet.
"He was ill-disciplined but what pleased us most was that our guys showed their fortitude, we won that period and I think that hurt England."