Blackpool remain eighth in the Hallmark Security League first division after sharing the points on Merseyside with a the club just a place and a point above them.
Ben Holmes gave Lairds the lead in the 16th minute but this was cancelled out by Conah Bishop just three minutes into the second half.
AFC went into the game after inflicting a comprehensive first defeat of the season on Silsden in the First Division Cup, though it was the hosts who started the strongerat the Kirklands Ground.
Lairds dominated much of the first half as AFC struggled to get into the game. A switch in formation for the second half saw Alex Taylor return and brought immediate improvements as Bishop equalised.
The second half was more even as both sides strived in vain for a winner. Winger Billy McKenna went closest for Blackpool, when his cross-shot looked to be goal-bound but struck a post.
Alex Caunce was forced off late on with a head injury and was replaced by James Corbett, who has signed for the club again.
Blackpool have had to settle for two points from their last three league games but will be aiming to return to winning ways at home to bottom club Nelson on Saturday, when they also seek to avenge last month’s penalty shoot-out defeat in the Macron Cup.
Blackpool: Kirkland, Nay, Betteridge, Caunce, Baird, Pickering, McKenna, Fishwick, Duffield, Bishop, Gregory; subs: Taylor, Muscroft, Hargreaves, Preece, Corbett.