The Pilgrims, missing a host of unavailable players, battled manfully at Brighouse Town but were beaten by a 73rd minute goal from the hosts.
Opting to using a 3-5-2 formation, the Pilgrims came close to picking up an excellent away point but were beaten late on.
Goalkeeper Marc Hipwell picked up an injury after only 20 minutes — but soldiered on and was only beaten 17 minutes from time following a rare slip from his otherwise watertight defence.
The match featured debuts for college scheme players Juris Kormis and Lemos Pereira.
Boston (3-5-2): Marc Hipwell; Scott Langan, Jordan Lote, Todd Devlin; Niall Delahoy, Joe Briers, Jake Beauchamp, Charley Sanders, Jake Platten; Jonny Butler, Juris Kormis (Lemos Pereira 60).