I don't have a major issue with a quarterback showing frustration with mental errors, although I would personally prefer that openly embarrassing the player be reserved for particularly egregious errors. If Janis runs a bad route and Rodgers throws a pick as a result, I'd expect him to be laid into.
Tretter not noticing a player jump into the neutral zone, which he obviously would have hiked the ball if he did, and being screamed at by his QB who is having an awful game himself, seems a bit like overkill to me. It's one thing to try to correct a teammate, it's another thing to just scream at them because you're already frustrated, which is clearly what happened in this case.
Berating a teammate on camera for a very minor and very innocent transgression isn't going to make them try harder or in any way be more productive. It's more likely to cause internal friction, like we subtly saw with Lang after the game.