Woodward wrote in his Mail on Sunday column that first five-eighths Marcus Smith's decision to kick the ball out showed that England's mentality was not in the same league as the other top teams in the world.
"I don't think New Zealand would have done that.
"At the finale, New Zealand were there for the taking. After losing Beauden Barrett to a yellow card, the All Blacks were on the ropes. That's what makes Smith's call so disappointing.
"Had this game been a World Cup final I would be of a different view. But it wasn't. It was an autumn international with nothing of huge significance riding on the result."
But as well as England did in the final 10 minutes to secure a draw, he said they should not paper over the first 70 minutes of the game.
"For long periods Eddie Jones' side were second best. England made basic errors and their discipline was poor."
Woodward said the final 10 minutes showed England could play running rugby, but he could not understand why they had to be 20 points down before going for broke.
"There was a big difference in the attacking play on show. England still have a lot of work to do there. Their tries came in a late salvo and with Barrett in the sin bin.
"New Zealand were a different beast, and their try from Rieko Ioane summed that up. It was a hugely impressive effort. When Ioane raced away to score, and then, Beauden Barrett slotted his drop goal, the game looked up for England.
"They deserve credit for coming back to earn a draw. But it could have been so much more and England will know that deep down."