The club has appointed premiership captain and third-year assistant Mark Bickley as caretaker coach for the remainder of the season, and has virtually ruled out appointing Craig in a director of coaching role.
CEO Steven Trigg told a media conference it was highly unlikely that the outgoing coach would take up such a position, but he said the club was reluctant to lose a person with "an extraordinary array of skills".
"You do not let those skills and experience go easily."
Craig said he "just knew it was time" to resign as coach.
"In the end you have to make a call about what is best for the club," he said.
"To continue would hurt the club, given the negativity and distraction that my own role has become. We have clearly underperformed this year and as senior coach, I take the responsibility for that."
The decision to resign had been made on Saturday but was not directly related to the 103-point thrashing from St Kilda the night before.
"It was just one small aspect of it," Craig said.
"A lot of other things came into it as well."
Adelaide chairman Rob Chapman, speaking on the club's website, praised Craig's decision and the legacy he would leave.
"Neil has, as always, demonstrated enormous integrity in making this decision. He's been true to his word that the club would come before his own career, and has made the call as we expected he would," Chapman said.
"I can't speak highly enough of Neil. He's made an extraordinary contribution to our club since 1997; and more particularly since taking over as coach midway through 2004.
"He has led the way in bettering the culture of our football team, and has driven standards and professionalism that has earned respect throughout the competition. And he has been an incredible role model in terms of the respect he's shown for his club and the game generally.
"Despite the disappointing results of late, Neil led us to five finals series, and re-established the list and the team to a strong and respected position."
League CEO Andrew Demetriou thanked the outgoing coach on his contribution to the game.
"Neil has been a tremendous coach and maximised every resource at his disposal to achieve the best both for his players and his club," Demetriou said.
"Neil has also been an outstanding contributor to our game with his willingness to look at the broader picture of football - how to improve the game, how to build the game and the duty of all players, coaches and officials to ensure the game is left in a better state for those who come after us.
"His work has been unstinting and football owes him a debt of gratitude."
Craig, who coached Adelaide in 166 games (for 92 wins) after taking over from predecessor Gary Ayres midway through 2004, was made a permanent member of staff prior to the start of the season, allowing either party to terminate the agreement with minimal notice.
Craig faced mounting pressure to retain his position at the club following the Crows' poor start to the season, and speculation over his future heightened after the demoralising loss to St Kilda.
Craig will now take a leave of absence until the end of October before he and the club decide where his future lies.
