Johnny Russell converted from the spot with four minutes to go to secure a 2-2 draw for the home side after referee Alan Muir ruled McGivern tripped Gary Mackay-Steven.
The on-loan Manchester City defender is not disputing the challenge but insists it took place outside the box - a view backed up by television replays.
He said: "I knew at the time when I stuck my leg out that I was giving away a free-kick.
"When I turned around and the referee was pointing to the spot I was shocked.
"I tried to have a word with the linesman and he was having none of it.
"I think the linesman has got to help the referee out there because I'm not sure what the referee's position was but the linesman should be level with the play.
"I've seen it back on the replay and you can clearly see I'm standing outside the box when I make the tackle so it's very disappointing."
He added: "I tried to tell the linesman it was clearly outside the box and he told me to get away.
"Whenever officials are like that you're not going to get much out of them. You've just got to get on with it."
Moments earlier, United claimed Russell had been fouled in the box by Paul Hanlon.
McGivern said: "The officials are there to make decisions and they've certainly got my one wrong.
"I've seen Paul's back as well and I don't think that was one either.
"If they've been influenced by the fans then that's a bit disappointing."
Hibs responded well after falling behind early on when goalkeeper Ben Williams' attempted clearance cannoned off the body of John Rankin and into the back of the net.
James McPake levelled for the visitors before a lovely strike from Leigh Griffiths handed them the lead until the late penalty call.
However, having picked up three points on the road against St Mirren in their last match, McGivern refused to be too downbeat ahead of Wednesday's game against Kilmarnock.
He said: "We've had two away games and picked up four points so if we can get a win on Wednesday it's a good week's work."
United boss Jackie McNamara said: "We were poor in the first half and were quite fortunate with the goal.
"I thought Griffiths was the difference between the two sides in the first half.
"But I thought we deserved at least a point for our second half performance."