A frustrated McGhee was sent to the stand as his side failed to recover from conceding three times in the opening nine minutes.
After the match the Dons manager said he felt referee Mike Tumilty got three major decisions wrong during a fiery 90 minutes at Tannadice.
He said: "For their penalty I have seen the replay and it did happen quickly but I felt it was a bad decision. At the second goal, for me David Goodwillie was distracting the goalkeeper and as far as I'm concerned the linesman or the fourth official could have helped the referee.
"I also thought we should have had a penalty after Kenneth had hauled Vernon to the ground but instead of that it was a free-kick against Vernon. I felt nothing went for us this afternoon but if you go three down so soon into the game you have to look at your own performance as well."
The Dons boss admitted frustration got the better of him after his side were denied the penalty just before the break.
He added: "It is a long time since I have been sent to the stand. I think the last time was when Steve Bruce and I got sent to the stand when Millwall played Birmingham.
"I like to think my behaviour is usually controlled and exemplary but when the ball landed at my feet, I couldn't help but boot it - it's a striker's instinct, although I missed the target!"