McGhee said he felt there had been a push by Kenny Deuchar on Dons keeper Jamie Langfield in the build-up to Saints equaliser by Liam Craig.
McInnes unsurprisingly saw things differently and belives the ref may have given the award in attempt to 'even things up'.
"There was a feeling of that in our dressing room," the Saints boss admitted. "I can understand why Aberdeen were feeling aggrieved.
"You often see a foul given with those sort of challenges on the goalkeeper but I think Kenny's eyes were only on the ball.
"At 1-1 I thought we were looking the better side and we should have left here with at least a point."
That said McIinnes was adamant that regardless of that the Dons should never have been awarded the spot kick which clinched the game.
"I felt there was definitely a foul on Danny Grainger in the build-up. Lee Miller grabbed Danny and spun him to gain an advantage in the box.
"The ball was played into the area 10 yards away from the incident and what has happened is Danny has tried to make up the ground after being fouled and, as he has run back, Lee has stopped and Danny has nowhere to go and it is a coming together.''
"The ref has said it was a push and a pull which it clearly wasn't. He has got it wrong and the linesman should see the foul by Lee Miller."
Nigerian internationalis Sone Aluko gave Aberdeen the lead witha superb solo effort in the first half but had to be substituted at half-time with astomach injury and McGhhe admitted its a cause for concern.
"We felt when Sone came back from his World Cup trip he had lost a lot of fitness and a lot of his edge and it has taken him until now to get that back.
"That goal will have done him a tremendous amount of good for his confidence as long as he recovers quickly from the injury.
"I would tend to think given his reaction to the injury that it wasn't trivial so it is a worry."
