Ok, I'm going to be honest, and this is coming from someone who would still have Karius over Mignolet.
First goal - Callum Wilson scored the exact same penalty (in the exact same position) just a week earlier against Arsenal. Why did Karius dive to his left when Wilson had put a penalty to his right just a week earlier? And why did the goalkeeping coach not do their homework as to where Wilson shoots when Bournemouth have penalties. I would put this one on both Karius and the goalkeeping coach. Although admittedly, even then Karius may not have saved it but at least do your homework on the penalty taker. Of course, it's better to not actually concede a penalty in the first place.
2nd goal - Karius should have done better. Especially since the ball seemed to bounce just before going in.
3rd goal - Karius could not have done anything.
4th goal - Karius' fault.
Look, I'm not having a pop at him. He's young, and he's a good goalkeeper in my eyes with qualities that Mignolet obviously didn't improve on his 3 years as a starter. I'm just replying to your point. I still believe he will go on to be a very good goalkeeper because I think he has the basic foundations to be one. We can't just lynch him after one bad performance, especially since Mignolet has had 3 years to prove himself.
Regarding pens, you can look at this both ways and seems many forget the gambler's fallacy. There is no 'right' side to dive which guarantees a penalty save because on the previous taker's pens.
The lad was BL goalie of the year, personally think some of you under-rate Mignolet's shot shopping on here, but if Klopp has backed the lad to be the keeper for the next few years you might as well get behind him, most young keepers are atrocious at commanding their box when they first move clubs anyway, so the fact he seems solid enough and may yet improve is a good deal.
Every GK mistake tends to have a chance at costing points, but it wasn't Karius who let the 3-1 lead slip by himself, was plenty of the game still left to influence at that point.