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.
"I had a couple of drinks in town with mates and basically I can recall everything that happened that night."
Hurricanes chief executive Avan Lee said after the game, about 11.30pm, there was a team meal and celebration in their team room at their hotel for Brad Shields' 100th cap.
Lee said that wrapped up about 1.30am, at which point Barrett went into town to meet his friend, Sam Casey. Two other Hurricanes players also went into town after the team event, with Lee saying there was no curfew in place.
By 5am on Saturday, Barrett was with Casey entering an unlocked house on Howe St which they thought was where one of their friends was hosting a party.
Upon finding it empty, they sat down to eat McDonald's they had purchased on the way to the house, at which point they were confronted by two women whose house it was.
"As soon as they've realised they're in the wrong house they've apologised and left the house," Lee said.
"I'm assuming they'd [the occupants] called the cops because they might have heard someone in their house," Barrett said.
"We walked into the house thinking it was Sam's mates, a few minutes later the penny dropped - he realised it wasn't his mate's house, we left and then the cops came."
Lee said it was an unfortunate mistake.
"It's clearly unfortunate the two of them have gone into a house and there are females in the house. We're obviously very sensitive about that and I can understand if they were uncomfortable."
A police spokesperson said they were called to a property on Howe St at 5.08am on Saturday after two men were found on a property.
"Police inquiries revealed the men had entered the property in error. Nil charges laid," the callout read.
Lee said Barrett had not broken any team rules, but they would have a discussion about the incident once he returned from All Blacks duty.
"There wasn't a curfew, but we obviously have certain expectations around alcohol and being out late. That's something we'll speak to Jordie about when he comes into camp.
"One of the key things for me was Jordie wasn't intoxicated. He'd certainly had a few beers, but he wasn't drunk, he wasn't disorderly.
"It a genuine mistake. I've spoken to Jordie twice, I know Jordie reasonably well and he's very trustworthy. He's young, he knows he's made a mistake, but there's nothing more to it than that. There was nothing sinister involved."
Casey told the New Zealand Herald they were "a couple of muppets making a stupid error after a few beers".
"We never intended to do anything wrong. The door was unlocked and we thought it was our mate's place, which it turns out is over the road."
Barrett returned to Wellington with the Hurricanes on Saturday morning, leaving the team hotel at 9am.
He will be in camp with the All Blacks for the next three weeks as they play France in three test matches, starting at Eden Park in Auckland next Saturday.