The club has written to competitions manager David Cookson to express its dissatisfaction after claiming the choice of |ends for the shootout had been pre-determined by home officials.
Cherries held the Terriers to a 3-3 draw after extra-time at the Galpharm Stadium before they bowed out 4-2 on penalties with the spot kicks taken in front of home supporters.
In a letter to the league, Cherries say boss Lee Bradbury was told ahead of kick-off that, should a shootout be required, it would take place at the home end of the ground.
Cherries claim the decision had been made by the Huddersfield safety officer on the grounds that some home supporters had purchased tickets for the Pink Link Stand at the away end.
It is alleged he declined to reveal how this had happened before he proposed a compromise whereby the toss of a coin would determine the end for the shootout, providing there was no trouble in the away end.
Cherries were adamant that no Huddersfield supporters had infiltrated the away end and said all travelling fans had been well policed and stewarded with no incidents reported during the game.
And while Cherries acknowledged some minor disturbances had occurred in the wing stands either side of the pitch nearest to the away end, they claim that only home supporters had been involved.
Subsequently, following the end of extra-time, the visitors fully expected the toss of a coin to determine at which end the penalty shootout would take place.
However, Cherries say match referee Neil Swarbrick informed Bradbury it would be staged at the home end upon instruction from the police and safety officer.
This, Cherries suggested in their letter, handed a considerable advantage to Huddersfield and had allowed a minority of home supporters to have a significant bearing on the outcome of the match.
When contacted by the Daily Echo yesterday, a spokesperson for Huddersfield Town said the club had not received any correspondence on the matter and did not wish to comment.
Cherries chairman Eddie Mitchell said: We don't want to make it sound like sour grapes, but we don't think it was fair to choose ends before the game because it gave them an advantage. It should have been determined by the toss of a coin. I am sure there would have been an outcry if somebody had tried to choose our end.
We feel strongly about it because it could have cost us a place at Old Trafford. If people don't voice their opinions then things like this could happen again. We want to make sure it doesn't happen to another team.
Mitchell added that Cherries wanted to wish well Huddersfield in their play-off final against Peterborough at Old Trafford on Sunday.