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.

Austin Okwor is reported to be part of a team investigating corruption within the judiciary. He is being treated in hospital for his wounds.
The attack happened in Port Harcourt on Saturday night, the Economic and Financial Crimes Commission said.
Last year several judges were arrested on suspicion of corruption in a nationwide sting operation.
President Muhammadu Buhari has prioritised the fight against corruption but critics say his administration has targeted only his political rivals.
Mr Okwor was surrounded by a gang who opened fire on him, Nigeria Bulletin reports.
Economic and Financial Crimes Commission spokesman Wilson Uwujaren said Mr Okwor had received threatening text messages in recent months.
"This incident underlines the hazards which operatives of the commission are daily exposed to in the discharge of their duties," Mr Uwujaren said in a statement.
In April President Buhari's office ordered an investigation after the head of the national intelligence agency was suspended over corruption allegations.
The president acted after anti-corruption officers found more than $43m (Â£34m) in a flat in the main city, Lagos.

In a nerve-stricken performance, Boreham Wood struggled to create anything at a quiet Meadow Park.
The Silkmen had the game's best chances, as Chris Holroyd tested Boreham Wood's James Russell before Kristian Dennis fired wide.
Harry White had the Wood's best chance, shooting over the bar as neither side could break the deadlock.
Glenavon will make an appeal after they were punished by the Irish FA for fielding suspended player David Elebert against Portadown on Boxing Day.
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A leading anti-corruption investigator in Nigeria has survived being shot multiple times, officials say.
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Boreham Wood's 0-0 draw at home to Macclesfield saw them fall into the National League relegation zone.