The Shamrock Park derby ended 2-2 but the IFA ordered that Glenavon forfeit the match with the bottom placed Ports awarded a 3-0 victory.
Glenavon believed Elebert had completed a suspension and was eligible to play.
The Glenavon board "unanimously agreed that the club would proceed with an appeal against this decision."
The Lurgan Blues were also hit with a £350 fine.
Elebert had been suspended for one game from 19 December for five bookings, three of which were picked up during reserve team matches.
Glenavon felt Elebert had completed the suspension when he sat out a reserve fixture - but IFA rules dictate that such suspensions apply to the "more senior team".
The Mourneview Park club said they had checked Elebert's eligibility with the governing body before including him in their team.
Glenavon will make an appeal after they were punished by the Irish FA for fielding suspended player David Elebert against Portadown on Boxing Day.