Jordan Burrow’s penalty on his debut meant Halifax went in level after Ricky Shakes’s opener, but second-half goals from debutants Jamie Lucas and Harry Crawford sealed the win.
The Halifax chief was unhappy with his side’s defending for all three goals, with captain Hamza Bencherif’s slip leading to the hosts’ second and Crawford getting the better of Matty Brown for his late effort.
Aspin said: “It’s very frustrating because I thought we were controlling the game when we conceded the first goal and then I felt we were getting on top when we conceded the second.
“They were both terrible goals to give away. Unfortunately, defensive mistakes have cost us.
“Their third goal is bad defending as well. All three goals should have been defended better.”
The game struggled to come to life until Shakes latched on to an innocuous long ball ahead of a static Halifax defence before lofting the ball over the onrushing Matt Glennon.
Burrow tucked away the equaliser from the spot with the last kick of the first-half before Halifax almost took the lead when Jake Hibbs’s free-kick hit the post shortly after the interval.
That proved the turning point as Bencherif’s misjudgment of another lofted pass allowed in Lucas before Crawford added the third after darting past Brown.
Boreham Wood: Russell, Nunn, Doe, Reynolds, Woodards, Lucas (Crawford 72), Shakes, C Clifford, B Clifford (Whichelow 78), Montgomery, Howell. Unused substitutes: Hill, Morais, Edwards.
FC Halifax Town: Glennon, Bolton, Bencherif (c), Brown, McManus, Macdonald (Bishop 68), Hibbs (Hughes 63), James, Whitehouse, Tuton, Burrow. Unused substitutes: Porter, Hutchison, Walker.
Referee: C Powell (Dorset).
Man of the match: Jordan Burrow.