The 21-year-old had played in the Hurricanes 30-14 loss to the Highlanders in the southern city on Friday night.
Barrett fronted media on Sunday morning at Wellington Airport, on his way to the All Blacks' camp in Auckland, saying: "I was not intoxicated". He apologised for the incident.
"I can't say I'm embarrassed by what's happened, I'm just disappointed with the events that have unfolded. I don't believe I've caused any harm to anyone.
"It was a human error, I walked into the wrong flat and then we left.