Albion went in front eight minutes before half-time through Tom Corner.
But Carsley struck twice in three minutes just after the break. And Regan Linney added a third for Brig in the 74th minute.
Elsewhere in the division, Clitheroe were held 2-2 at home by Ossett Town, and Kendal Town lost 2-1 at Colne.
In the NPL Premier Division, Phil Brown’s Lancaster City were beaten 3-2 at Grantham Town.
Jordan Hempenstall put Town in front in the third minute but the Dollies turned it around with strikes from Steve Williams (7) and PNE loanee Melle Meulensteen (11).
Two Curtis Burrows goals in the second half won it for Grantham.
AFC Fylde booked their place in the second round of the FA Cup for the first time after beating Kidderminster Harriers 4-2.
In the NWCL Premier Division, Burscough lost 2-0 at Hanley Town and Charnock Richard went down 1-0 at home to Abbey Hey.
In the National League North, Southport failed to beat bottom club North Ferriby United and had to settle for a 2-2 draw.
After new signing Josh Hime had missed an open goal in the 21st minute, Mark Gray put the visitors in front on the half-hour.
Steve Schmacher intercepted a wayward clearance and levelled before the break.
Jordan Hallam, on loan from Sheffield United, put Port in front in the 51st minute, converting Brad Jackson’s cross, but Kuda Muskwe equalised on the hour.