To do it at Chelsea was a mistake as well, as he played for them it was highlighted, i'm sure its something he regrets, he looked embarrassed getting up after he dived.
The stupid thing is I have see loads of defenders grab his shirt and wrap arms around him in the box, but he rarely went over and preferred to keep the ball and try and score, but when he doesn't score, in effect he's penalised as he didn't maximise the contact and go down for the penalty.
The danger is if you get a reputation for diving, it puts doubts in the refs mind and you might not get decisions in the future, I'm guessing that's part of Klopp's concern.