However, neither of the assistant referees, Mike Fraser and James Doleman, nor referee Paul Williams or TMO Brendon Pickerill picked up on the oversight, much to the dismay of Barrett, the commentators and the crowd at Wellington's Sky Stadium.
Numerous fans have taken to Twitter to express their outrage at the decision, with some describing it as "shocking" and "disgusting".
One fans joked that it "seems appropriate the touch judges are sponsored by spec savers", while others argued the officials got it right as the ball sailed over the top of the upright, which they believed meant it would have hit the post if it was lower.
Another Twitter user wondered if Hurricanes skipper Ardie Savea could have used his captain's call on the decision.
Respected rugby journalist and broadcaster Nigel Yalden, meanwhile, said the conversion should be awarded after the fact as the resulting play – a re-start back at halfway – is the same regardless of whether the conversion is successful or not.
In the end, though, the conversion wouldn't have made a difference, as the Blues ended up running out 31-16 winners after Rieko Ioane and Otere Black combined to score 10 points in the final five minutes.
Barrett was thrust into the limelight earlier in the match after he landed two monstrous penalty goals from near halfway to give the Hurricanes an 11-7 lead at half-time.
However, the Wellington franchise find themselves at the bottom of the standings, trailing the fourth-placed Highlanders on points difference.
This article first appeared on RugbyPass and is republished with permission.