Howlett, 29, was detained in the early hours of Monday morning following an incident outside the Hilton hotel at Heathrow airport which resulted in damage to two parked cars. He was later bailed to return later this month.
A number of All Blacks were staying at the hotel as they waited for flights home following their shock defeat to France in the World Cup quarter-final on Saturday.
Reports indicate the players had run up a bar bill over Â£12,000 - but New Zealand team manager Darren Shand confirmed Howlett was the only player involved in the incident.
Howlett took the unusual step of issuing a video message in which he said: "Firstly I'd like to say I am sorry for what has happened. I am embarrassed that the events of one evening have led to me being in this situation.
"It was a little bit of tomfoolery.
"I apologise to the people back home, family and friends, the New Zealand public, fans and my team-mates.
"I am working with the police at the moment to contact owners and fix what I have done wrong.
"It is an embarrassing time but I do take sole responsibility. There was drink involved and it is not an excuse.
"There was no intent to cause anybody or anything any harm whatsoever."
Howlett is among several players to have remained in Europe following New Zealand's 20-18 defeat in Cardiff, which confirmed their worst World Cup performance.
He is scheduled to join Irish province Munster on a two-and-a-half year contract from January 1.
The New Zealand Rugby Union have launched their own investigation into the incident.
Shand said: "We are waiting for the police to conclude their inquiries. Once that occurs, we will initiate our own process to look into the incident and related issues," said Shand.
"It is a serious matter and we are concerned that something of this nature has occurred at what is already a disappointing time for the team and for our supporters."
Howlett is New Zealand's record try-scorer with 49 in 62 Tests, having overtake Christian Cullen during the World Cup.