Cowan (26) faces a misconduct hearing in Wellington today after being arrested outside an Invercargill hotel at 3.40am on Sunday and charged with disorderly behaviour likely to cause violence.
All Blacks manager Darren Shand told the Otago Daily Times there was a range of penalties to consider, from a warning to termination of his contract.
The team felt Cowan had "let them down".
Shand would not prejudge the outcome of the hearing.
"He [Cowan] is worried for his future and what that future might be," Shand said.
"He let himself down and we all feel the pain. I think the group feels let down."
The hearing would involve Cowan giving a full explanation of what happened before his arrest on Sunday.
Evidence would be presented by the police and other witnesses to the incident.
Shand acknowledged Cowan had an issue with alcohol, and incidents like this were "doubly frustrating" in efforts to win back fans after the World Cup disappointment last year.
Cowan's recent conduct showed a "clear pattern of behaviour indicating he doesn't make good decisions when he's been drinking".
Shand said he was aware Cowan was remanded for diversion until August on a disorderly conduct charge stemming from an incident in Dunedin on May 10.
The All Blacks play the Springboks in Wellington on Saturday night, and Cowan is expected to be named on the bench.
Shand said Cowan was still with the team but was feeling "empty" at the moment.
"There are expectations what these guys should do during the bye week [Cowan played club rugby for Mataura on Saturday afternoon].
"But we can't bodyguard them 24/7. We can't walk around the country with them, holding their hands."
Cowan had not addressed the players as a group, but had spoken to management about the incident.
It was procedure to wait for any court process to conclude before taking action, but All Blacks management wanted to resolve the issue quickly in the interests of both parties.
Cowan will have his representative, Tom Downey, at the hearing, and Shand will be accompanied by New Zealand Rugby Union professional services manager Neil Sorenson.
Shand expected a decision to be released straight after the hearing.
Cowan could not be contacted yesterday.
Southland Rugby Football Union chief executive Roger Clark said he spoke to Cowan on Sunday and said yesterday he supported the All Black procedure.
In 2005, the New Zealand Rugby Union suspended Cowan for a week when he was sent home early from a Junior All Blacks tour of Australia after an incident in a bar.
