Let's be accurate shall we:
"A tackle occurs when the ball carrier is held by one or more opponents and is brought to ground.
...
A ball carrier who is not held is not a tackled player and a tackle has not taken place."
I also consider this to be an important aspect of the rule:
"A tackle can only take place in the field of play."
This is getting interesting. The field of play being defined by the zone surrounded by the touch lines and the in-goal lines, the zone between the in-goal lines and dead-ball lines is not part of the field of play. The contact between Barrett and Carr takes place in said zone, so the word tackle has no meaning in that situation. In fact, it could have been anything else under different circumstances. If the ref had ruled a high contact (i.e. foul play), Barrett could have been sent to the naughty chair for the rest of the match, but this is still no tackle. It is obvious under any angle that Barrett was only looking to connect with the ball, and because refereeing is a matter of interpretation (thankfully), the try was awarded.