Here's a picture I took at Anfield towards the end of the match.
Yes their corporate fans had started leaving, either for more hospitality, or making their way home. But the rest of The Liverpool fans stayed until the final whistle. You can just make out the corner of the KOP.
TBH, today was a lot better than it has been. I think Pep's message about fans staying until the end of the match and supporting the team is getting across.
Saying that, there were fans in East stand lower who were leaving with 10 minutes to go. They weren't going to the toilet.