The Lions' overall record against the All Blacks now shows just six victories from 38 starts.
New Zealand confirmed the tourists' demise through touchdowns from skipper Tana Umaga (2), his midfield partner Conrad Smith, wing Rico Gear and lock Ali Williams.
Fly-half newcomer Luke McAlister booted all five conversions and landed a penalty, and the Lions could only respond through a Lewis Moody try and 14 points from goalkicker Stephen Jones.
Woodward's adventure ended with another defeat and more misery for 20,000 travelling Lions fans, but England star Lewsey offered a philosophical view of the series.
"We were pretty ashamed of our first-Test performance, and in the second Test we gave it everything but just weren't good enough and got beaten by a better side," he said.
"We tried to take the lessons on board, and we tried to play with ball in hand a bit more, but it takes time to develop. Natural ability will only get you so far, and you have to put your hand up and say they were better than us.
"They are leading the way in terms of the way the game is played at the moment, but you cannot blame anyone for their effort.
"If you are not good enough, then you've just got to say fair enough, learn the lessons and tip your hat to the opposition.
"My biggest disappointment is that this group of players is too talented and too good to go down in history as being a bunch of players that lost a series 3-0, but it has happened and we have got to get on with it," Lewsey added.
"At the moment, you have to say New Zealand are a pretty smooth outfit, but I don't think they are unbeatable by any stretch of the imagination.
"It will be interesting to see how they fare in the Tri-Nations. I am sure Australia won't fear them, and South Africa always do well against the All Blacks, so we will wait and see."