Yes, it goes without saying that a club with a huge world wide fan base will have its share of (genuinely) racist fans.
However, this phenomenon (posting abusive shit on social media as an apparent reaction to players missing penalties) seems to be - well - real. IIRC it was established that most of the users who posted abuse after England's Euro shootout were not based in England and most likely not England fans at all. *
It really isn't surprising that trolls (kids, like as not) have jumped on this despicable trend - just look at the response it generates.
* I didn't remember correctly: this was rumoured to be the case but later proved incorrect. What was established was that a lot of abusive posts were made by people who very likely weren't England fans - but the majority of the abusive posts came from users within the UK, so I was wrong about that.