The Millers somehow managed to snatch defeat from the jaws of victory at Brighouse on Saturday.
Two stoppage time goals from the hosts ensured Roy Soule’s side went home empty-handed.
Brighouse started the brighter as they peppered Peter Collinge’s goal with a couple of efforts.
However, Daniel Grimshaw was on hand to give the visitors a 21st-minute lead, with a powerful long-range effort.
Brighouse then netted twice in five minutes to ensure they took a 2-1 lead into the interval; Boafo and Frankland with the goals.
New Mills played much the better football in the second half and Grimshaw saw his shot flash just over, before Daniel Douglas-Pringle equalised.
The Millers then stepped up a gear and went 3-2 in front a few minutes later, with Douglas-Pringle heading home.
It remained this way until 20 seconds of normal time remaining, when the Millers lost possession and Tyrone Gay’s long shot made it 3-3.
Then from the restart, Brighouse pinched possession again and James Hurtley capitalised to break Millers’ hearts.
New Mills are in FA Trophy action on Saturday, at home to Ossett Albion.