Allen had only started 24 first-team games for Gloucester before winning promotion to the England side to face the world's number one side in front of a record 82,000 crowd.
Allen kept his composure and created the opening for Jamie Noon - who earlier had a perfectly good try disallowed - to score England's first of the afternoon.
But memories of his Test debut will be dominated by two high-profile mistakes, both of which led directly to New Zealand touchdowns.
Joe Rokocoko picked off Allen's speculative midfield pass shortly before the interval and raced 50 yards to score the second of New Zealand's three first-half tries.
And, 10 minutes into the second period, Allen slipped off a weak tackle as Carter scored a classy fourth.
"At international level, if you make silly mistakes you get punished and New Zealand are a world-class team and you can't let them do that. That's what I have learned," Allen said.
"You have got to be hard on yourself to get better. The little things have got to be spot-on on the day.
"A few things didn't go right for me but I can take a few positives and I think I did alright. Andy said it was nothing to be ashamed of.
"He said to me 'well done, it was a good debut at Twickenham, take the positives from it, you did very well'.
"Hopefully, there will be many more to come. I have got to put this behind me now and go forward. You have to positive on everything.
"I'm disappointed with the result, the whole team is, but we can't dwell on it. We were beaten by the better team."
England's cause was not helped by Charlie Hodgson missing a string of goal attempts and Noon's early try being disallowed.
That would have put England 5-3 up after just four minutes.
But the call went New Zealand's way and the All Blacks were merciless.