Director of sport Chris Turner insists Hartlepool are innocent after the club were charged by the Football Association for fielding an ineligible player during Easter Monday's win over Brighton.
Seagulls boss Gus Poyet feels his side should be awarded the points and warned the FA "have to be careful with the decision they make''.
Pools selected midfielder Gary Liddle in the 2-0 League One victory at Victoria Park when he should have been serving a two-match ban for collecting his 10th yellow card in the previous game at Leyton Orient.
Liddle has also been charged and both he and the club have until April 26 to respond to the FA.
Hartlepool sit four points above the relegation zone in 17th place and any possible points deduction would hinder their chances of avoiding the drop.
However, Turner revealed Pools were "informed by the FA on Tuesday morning he was suspended for the Brighton game'' and hopes "common sense prevails''.
Turner added in The Journal: "I believe we are innocent and three or four different things have conspired to the situation and the FA, so I am led to believe, are understanding about it.
"The bottom line is, what manager or coach in the world would select a player to play in a team if he was not eligible to play? It is less than Sunday league stuff. End of story.''
With half a dozen teams involved in a relegation battle, Poyet feels "for the sake of fair competition'' the points should be awarded to Brighton.
Poyet told his club's official website: "I am sure Hartlepool did not realise he was suspended. It was not a case of cheating, but they made a mistake and that player should not have been on the pitch so the three points should go to the opposition.
"They cannot just deduct the points from Hartlepool. For the sake of fair competition we should be awarded them. All teams play 46 games in a season so it would be unfair if we only played 45 matches.
"The Football League has to be careful with the decision they make. It does not matter if they did it with intention or not, the only decision they can make in this instance - and I would say the same if my team were the guilty party - is to give the three points to the opposition.''