It would be great for your children to see you make mistakes and how you react. Think out loud how you process and feel when you make a mistake. Start now when they're 4-5, as it will go a long way to how they feel about themselves when they're 8-10 and beyond.
Not only are some children wanting to be perfect and showing perfectionism issue, I'm sure you know also, they are "intensely" trying to be perfect too. And can you imagine a 4-5 year old dealing with their intensity/perfectionism -- there is no way they know how to deal with it unless someone teaches them.
I have to add, since I have seen other ppl do, not saying any one here does or doesn't, but telling someone to stop feeling a certain emotion, like "stop being so intense", "don't be so dramatic" or "what is wrong with you" is very damaging to these sensitive souls. I believe in acknowledging that they are just the types of people that feel intensely (and there are a lot of other people like that, maybe mommy is like that too) and this is how we learn to manage it... etc etc.
Learning to make fun of our own mistakes is great too.