Aberdeen boss Jim Goodwin fumed at John Beaton and told the referee he'd missed an "easy decision" as he claimed Charlie Adam "struck" Lewis Ferguson in the face twice.
The Dons took the lead against Dundee twice thanks to goals from Calvin Ramsay and Ross McCrorie but were pegged back twice by Mark McGhee's men.
Jordan McGhee found the net before Danny Mullen grabbed a late equaliser in the four-goal thriller.
It was the build-up to their first goal the provoked the ire of the Aberdeen gaffer after the full-time whistle.
He claims that contract was made with Ferguson's face by Adam, before the Dee skipper stepped up to curl the free-kick into the box for McGhee's goal.
Raging Goodwin told BBC Sportsound: "We should have been two or three goals to the better after the opening 45 minutes.
"We do well to get ourselves in front and then we score a good second goal, but we've conceded two extremely poor free-kicks.
"I can't not mention the build up to the first goal, because Charlie Adam has clearly struck Lewis Ferguson twice in the face which should have been a foul for us.
"I'm not saying it should have been a red card, but it certainly should have been a free-kick for Lewis Ferguson.
"John Beaton has got a perfect view of it. It's a very easy decision I think. Five seconds after that they get the opportunity from the free-kick we give away, and that ends up in the back of our net.
"With all of that said, we need to defend the cross better. We need to defend both crosses better. We need to take responsibility in the key moments, and if we had done that we would've won the game."