The Pilgrims trailed Altrincham for large swathes of the game - although Luke Horne equalised with 11 minutes to play.
Horne subsequently hit the post - and Altrincham took full advantage with two goals in stoppage time.
Boston: Cameron Fox, Ellis Perry-Burdett (Oliver Fields 88), Josh Doran, Will Langford, Finley Ging (Charlie Brooks 77), Taylor Jaine, JJ Ward, Kris Zaluzinskis (Flynn Slater 72), Nathan Bowen (Rueben Fogg 57), Joe Wilkinson (Jake Henderson 57), Luke Horne.
Referee: Trevor Basker.
PIC: Steve Davies.