"Although Garcès was within a few metres of Lawes at the time of the incident, he appeared to go against the directive by consulting with Jonker.
"Allowing Jonker to make the final decision would also seem to contravene the directive that requires "compelling evidence" for the TMO to intervene with World Rugby considering Lawes to have been marginally offside.
"Ultimately however, the governing body believes a number of mitigating factors meant Garcès was within his rights to defer the final decision to the TMO, chiefly the poor weather which made visibility of Twickenham's big screens more difficult."
All Blacks coach Steve Hansen praised the match officials after his side's 16-15 victory, saying they were brave to make what he called the "right decision".
"There was no doubt he was offside," said Hansen.
"He was just about in the halfback's back pocket. What was going through my mind was are they going to be brave enough to make the right decision and they were so it was good."
Meanwhile, England coach Eddie Jones was magnanimous in defeat and refused to blame the referees.
"I don't comment on those decisions I leave that up to that guy and if he can't make the right decision with 10 replays then who can," Jones said after the test.
"Sometimes the game loves you sometimes the game doesn't love you. You've got to accept that if you stay in the fight long enough the game will love you. We're prepared to stay in the game so we'll get some love further down the track don't worry."
The All Blacks will next face Ireland in Dublin on Sunday.