The 48-year-old made the decision following a run of results that has left the Monkey Hangers bottom of the League One table.
"He decided that it was in the best interests of the club that he stood down from his position as manager," read a statement on the club's official website.
"Neale stated that he had been very disappointed with the results achieved since the start of the season and, although in several games luck had been against the team, he nevertheless believes they can move on and secure League One status with someone else leading the campaign.
"The club wishes to thank Neale for his commitment and dedication, and wishes him every success in his return to Scotland."
Micky Barron has been placed in temporary charge.