AFC went to Derbyshire in search of a third successive Hallmark Security League win but were well beaten.
The visitors were forced into changes and manager Dave Worthington handed first starts to two new signings, defender Alex Caunce and midfielder Zack Hargreaves.
Playing up the slope in the first half, AFC found themselves two goals down early on as they did against Didsbury and Chorlton in the FA Vase the previous weekend.
Defender Darcy O’Connor opened the scoring after eight minutes and the Millers doubled their lead six minutes later, when Dennis Sherriff cashed in on a defensive error.
AFC rallied as the fit-again Billy McKenna and Connah Bishop had good chances. They pulled a goal back on the half-hour, when Kit Gregory followed a superb turn on the edge of the box with a cool finish.
The rest of the half was more even and the lively Gregory went close to a second from new boy Hargreaves’ fine through-ball.
However, just two minutes into the second half Nathan Neequaye restored New Mills’ two-goal advantage.
This seemed to break AFC’s spirit somewhat and George Blackwell made it four on 71 minutes.
A disappointed Worthington said: “We have to be better at starting games. Last week we were 2-0 down after 14 minutes, and it was exactly the same here.
“Too many players were not at the right intensity at the start of the game, which then set the tone. We gave the Millers too much time on the ball and it gave them confidence.
“We knew there would be hard days and there will be more to come, but we will get there and there will be positive days.
“This was our worst performance of the season but we will keep working hard to get things right.
“I believe we can be competitive in this league but it will require a lot of hard work from the lads and a high level of commitment from everyone at the club on and off the pitch.”
Worthington also praised the sizeable away contingent who boosted the crowd to 135.
AFC will be at home to Cammell Laird 1907 this Saturday in a game brought forward from November.
Blackpool: Kirkland, Baird, Betteridge, Caunce, Taylor, Pickering, McKenna, Hargreaves, Ngamba, Gregory, Bishop; subs: Nay, Purdon, Preece, Fishwick, Speight.