Both Priestman and Gordon were judged to have denied a goal-scoring opportunity after Beaton went to the monitor.
And Aston Villa’s 83-times capped McGinn, whose brother Paul captained Motherwell, said on social media: “I’ve sent you to the screen let’s send you to an angle from the North Sea to back it up.
“Scottish var is a mess.”
In his post-match interview, Motherwell manager Jens Berthel Askou told BBC Scotland: “We get Liam Gordon sent off in a decision that is a mystery to me and will remain a mystery to me because there are two players covering behind him who will, without a shadow of a doubt, get in his way or at least make sure it’s never a very obvious goal chance.”
The Scottish FA have been approached for comment.
The Priestman and Gordon red cards follow similar incidents in Dundee United’s Tuesday cup win over Spartans and Falkirk’s Premiership defeat by United on Saturday.