Adelaide players Brad Crouch and Tyson Stengle were caught with an illicit drug, believed to be cocaine, when pulled over by police early on Monday.
The pair, who face fines and possible suspension from the AFL, were in a taxi in Adelaide's central business district when stopped by police at 5.15am CDT.
Police won't charge the pair but have referred them to counselling.
Crouch, a newly-turned free agent weighing offers to join rival clubs, and Stengle, who the Crows banned earlier in the year for drink driving, face certain sanctions from their club and the league.
"They are really embarrassed, disappointed," Adelaide's head of football Adam Kelly told reporters.
"They feel like they have let the club down, their teammates down, our members and supporters - which they have."
Kelly said the Crows were still seeking specifics over the incident at Grenfell St in central Adelaide.
"The club leaders are going to have to come together and discuss it and make a decision on what a club sanction might be," he said.
Stengle in April was banned by the Crows for four games after police caught him drink driving and driving an unregistered car.
The 21-year-old was due to appear in Adelaide Magistrates Court next month to answer those charges.
"It's fairly obvious he hasn't had a good six months and has made some really poor decisions," Kelly said.
Crouch has fallen off contract with the Crows, becoming a free agent when Adelaide's season ended nine days ago.
Adelaide's 2019 club champion, Crouch was to have met with Crows management this week to decide his future.
Those talks have now been paused.
"We need to work through these issues before we start talking about contracts," Kelly said.
Crouch and Stengle, in a statement released by their management company, said they unconditionally accepted responsibility for their actions.
"We accept that our error of judgement is not in line with community expectations nor the high standards we set for ourselves," the joint statement issued by W Sports and Media said.
"In this regard, we are committed to the counselling process that SA Police has implemented to manage this and will continue to cooperate with our club as required."
Crouch and Stengle face fines of up to $5000 among other sanctions.
Under the AFL's drugs policy, a player is issued a strike when found to possess or use an illicit drug or returns a positive test for such sustances.
A player will receive a $5000 fine for a first strike while also undergoing counselling and target testing.
In the event of a second strike, a player's name is made public and he is suspended for four games.
A third strike incurs a 12-match suspension.
An anti-doping violation, leading to year-long bans, is only issued when a player tests positive to illicit drugs on a match day.