The Czech striker was hauled off just 34 minutes into Wednesday’s 2-1 defeat against Dundee with Levein describing his player’s performance as “rubbish” after the game.
The manager went on to criticise Vanecek’s fitness, saying he hadn’t turned up to the club’s winter training camp in proper shape.
Thompson believes this sort of scolding should have taken place behind closed doors.
He also questioned why Levein picked the player in the first place if he wasn’t happy with his fitness.
Levein said: “Why on earth would you start a player who is not fit enough? If he’s not fit enough, start Stevie MacLean.”
“To suffer the indignity of being whipped off the first place is humiliating enough.
“Talk about man-management. That’s as poor man-management as I’ve ever seen.
“There are hundreds of times I’ve merited criticism and I’ve been told it privately. That’s an entirely different matter.”