The Manchester City loanee fouled Dundee United's Gary Mackay-Steven late in the clash at Tannadice Park with McNeillie awarding a penalty to the Terrors which was converted by Johnny Russell to force a 2-2 draw.
McGivern was aware he had given away a foul but was horrified to see that Muir had not overturned the initial decision which eventually cost Hibs maximum points.
"The officials are there to make decisions and in my case they've got it wrong," he said.
"If they were influenced by the fans that would be disappointing.
"I knew at the time when I stuck my leg out I would give away a free-kick. But I was shocked when the ref gave a penalty.
"I think that the linesman has got to help him out because he should be level with play.
"But they were having none of it when I spoke to them. They just told me to go away. It's very disappointing.
"The league is tight so every point counts but we've taken four points from the last two away games and we want to keep it going on Wednesday."