McGhee was furious that Beaton and his assistants failed to award a goal when Dundee keeper David Mitchell carried the ball over his goal line after Scott McDonald’s overhit 15th minute cross.
This incident came around 10 months after the same referee controversially gave Dundee a late penalty for Chris Cadden’s innocuous challenge following a corner, from which Dundee scored to earn a controversial late draw.
“He (the referee) never gave an explanation for his decision not to award a goal,” McGhee said.
“And he never gave an explanation last season when he gave a penalty against Chris Cadden.
“It’s the linesman as well. He’s got to help him. There’s two of them there and they can’t see it. I don’t understand it.
“But the worst decision I’ve seen is when he awarded a penalty against Cadden here last season.
“I don’t think today’s decision caused us to lose the game but I think it caused us not to win the game.
“I think at that point we were starting to undermine them. They were getting a bit of stick from the crowd.
“They were under pressure and the disallowed goal came at the point when we could have gone on and won the game, but it wasn’t given.
“That was the disappointing thing and then we conceded a goal.”
McGhee said that his side’s poor first half display against Dundee on Saturday had given them a major handicap which sadly they couldn’t overhaul.
He added: “In the second half we just couldn’t get going but the first half was a disappointment. We didn’t play well enough.
“We set ourselves up for what happened in the second half by being a goal down.
“In the first half we planned to get down the sides of them and we kept going inside, trying to play balls into the centre forwards instead of going down the sides.
“I don’t think we worked hard enough in wide areas to get behind them.
“Eventually we got the breakthrough and we’d have liked that goal obviously.”