The Pilgrims' hopes of reaching the competition proper were ended by National League U19 Alliance Academy Division North rivals Solihull Moors.
Second half goals from Kyle Moseley and Billy Fielding sealed the deal for Mike Fowler's side at the Jakemans Community Stadium.
Boston: Zach Marsh, Finley Hipkin, Oliver Houlston (Alex Van-Tam 90), Jake Thompson, Charlie Brooks, Kirils Snikeris, Toby Cotton (Dennis Matei 68), Will Langford, Will Pettitt, Zac Hardy (Oliver Callaby 29), Rhys Smaller (Daniel Bridges 78). Subs (not used): Charles Doble, Dominic Chew, Austin Barker (gk).
Referee: Peter Brothwell.
Attendance: 228.