My 7yr old son (soon to be 8) is like that too. I also tried to explain that people make mistakes, which also didn't work. So, my husband and I started pointing out times when we made mistakes and how hard it was, the struggle and frustration we felt. (Everyone gets a good chuckle.) My husband and I have also had to look at how we display our frustration when we face a challenge. (It's unsettling how our sons are little mirrors, as they reflect back our own behaviors.
Also, when he's in the throws of frustration, I just hug him, let him cry and tell him that I understand that it's frustrating when you don't get something that you think you should be able to. Most of the time that works. And, sometimes he's just so hard on himself that I just have to let him cry. (He started hitting himself on the head, so I ban that.)
When he's in a really bad way, I'll sit him down in a private, quiet place and ask him to use his words to explain why he feels so bad. After he feels like I've heard what he has to say, he calms down and I try to reframe his desire to get things right, in a positive light, and list all the reasons why I love him.
With those strategies, he's had less big emotional break outs and is more apt to express his frustration in words before it gets to the point of crying and major drama.