mine will be 8 in Nov. He is a bit like this, but more generally. He feels the fact he is near the bottom of the class and he feels failure easily (he dropped the baton on Sports' Day which the next kid gave him a very hard time over even though I think it was his fault it was dropped and although their class won Sports' Day overall, ds1 could not enjoy the victory because he was still reliving the baton pass until he went to bed that night).
What did the 'good' teacher do, do you think, to help him relax? Lots of praise.
If he is a perfectionist, I would avoid phrases like 'do your best' as 'best' can be limitless. I would also just try and get him interested in other things so that he sees there can be achievement in areas like art, music, writing, sports, digging up dinosaurs or whatever may pique his interest.
I think constantly re-iterating that you can't be the best at everything, that everyone has different talents, that everyone learns at different paces. It sometimes just takes a lot of repeating, but it is going in somewhere and it will come out the other side.