The Crows' finals chances ended with the defeat after the goal umpire awarded a behind rather than a goal by Ben Keays, which would have given Adelaide the lead with just over a minute to play in Saturday night's Adelaide Oval clash.
The umpire signalled the ball hit a post and didn't seek a video review - which McLachlan said on Sunday he should have done.
"There was a goal umpiring decision that should have been reviewed and it was a mistake," McLachlan told reporters.
"I want to say conclusively that if the decision had been reviewed, it would have been overturned and it would have been a goal.
"It's a human error that happens repeatedly through games and across the course of the year but this is an error that, given the context and the moment, was of great consequence.
"I want to acknowledge that was a mistake and want to take accountability for the mistake on behalf of the league."
The 13th-placed Crows are two wins outside the top eight with one game remaining, an away trip to play struggling West Coast.
The goal umpire at the centre of the controversy won't be available for selection for the rest of the AFL season.
The AFL said the Crows had been nothing but professional in their dealings with the league.
Adelaide chief executiveTim Silvers said the admission of error did not lessen the frustration and disappointment shared by everyone involved with the club.
"Human error is, and always will be, part of football and we recognise our own performance in the first half of the season-defining game was not at the standard we expect either," Silvers said.
"We are also extremely proud of our players' effort, commitment and never-give-up attitude, which was again on show.
"The failure to video review the scoring attempt in question is inexplicable given the enormity of the moment, not just for that game but also what it meant for our finals chances and those of other teams in the competition.
"Having spoken to the AFL and with no further avenues to explore, we have no choice other than to turn our focus to the final home and away match of the season."
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