The FA Trophy finalists came very close to securing their status in the fifth tier deep into injury time when Waide Fairhurst's header hit the post.
Scott McManus fired Halifax in front before the break but Danny Rowe equalised with a deflected shot from inside the box.
The Shaymen dropped into the bottom four after Guiseley beat Torquay 4-3.
Halifax Town were relegated from the National League after failing to beat Macclesfield at The Shay.