Why is it something that you feel needs fixing? Caring deeply about something you care about is a good thing, it shows pride in your work/craft. Sure, nothing and nobody is ever 100% perfect 100% of the time but none the less I can assure you that people in other fields often feel the same way about the same things (bugs, faults, design errors, something missed in an audit etc).
In my opinion you are showing the attributes of a great employee and with your attitude I would hire someone like yourself in a heartbeat.
I have come across both those that care deeply and those that shrug off errors as 'meh, shit happens' and I can honestly state that the good ones cared while the ones that had the 'shrug - so what' attitudes were mediocre (at best). In one of my more uncharitable and judgemental moments it struck me that their attitude of not caring was because they had so much prior practice at dealing with shit-that-went-wrong issues that it was nothing new.