Steve Welsh's young side, which featured six members of the club's current under-16s team, competed well at the Scholars Ground, but were up against it after conceding three times before the break.
Tom Benton, Daniel Worthington, Joe Cain, Corey Newman and Miles Lynch all started the game, while Joe Searson appeared as a second half substitute.
Boston (4-4-2): Tom Benton; Daniel Worthington, Joe Cain, Todd Devlin, Corey Newman (Charlie Melville 55); Miles Lynch, Jacob Pease, Jordan Sowerby, Lewis McKue; Leon Squire (Joe Searson 60), Juris Kormis.