Lee Morris’ side had hoped to build on their opening day win at Teversal but the visitors ran out 2-0 winners at the Marra Falcons Stadium.
Nathan Perks was sent clear and rounded Armthorpe goalkeeper Joe Mellor to put Nostell ahead after 26 minutes.
Welfare defender Owen Fieldsend might have done better with three headed chances, while Matty Hughes dragged a shot wide and Steve Garner also shot just over for the hosts.
Armthorpe were left to rue their missed chances when they were caught on the break and Annes Younis crossed for Perks to tap home Nostell’s second after 87 minutes.
Armthorpe host Rainworth Miners Welfare on Wednesday night (7.45pm).
Meanwhile, striker Adam Baskerville has returned to Armthorpe just months after leaving the club.
Baskerville left to join Hallam over the summer but has opted to return to Welfare where his record is 21 goals in 44 first team appearances.