The Pilgrims were beaten 5-2 by Long Eaton United despite holding a 2-1 advantage with 18 minutes to play, courtesy of Jackson's 37th and 62nd minute strikes, which sandwiched his penalty being saved by home keeper Jake Beresford-Allen.
Benni Wilson scored a hat-trick for the home side, with James Gale and Reece Widdowson also on target.
Boston (4-3-3): Jake Frestle; Nathan Stevens (Arron Bailey 80), Brogan Horniman, Daniel Fisher, Jordan Elston; Finlay Armond, Dan Richards, Joe Hardstaff (Ben Johnson 75); Henry Beedham (Jack Bastow 57), Will Jackson, Xander Crashley. Subs (not used): Joe Melson, Owen Sheriff, Harry Chapman (gk).
Referee: Ian Jackson.