I think you first have to do some serious self-searching to understand what is at the core of your fear of your children's success to really know how to address it. If it comes from seeing a propensity towards arrogance and superiority, you'd definitely address how you handled it much differently than if it came from familial comments that made you worried about how others would react to your childs' successes, etc.
For my older two, being in a competitive sport that challenged them to beat their own last best score as well as competing against peers helped build a lot of character about how to handle their successes and failures. And because there were two siblings competing in the same sport, learning to temper one's own joy of success with sympathy for a sibling's bad performance also came with the territory. Maybe because it was physical and not mental, they were also far more comfortable being proud of their own success than they ever were in the academic realm.
Don't beat yourself up for it, though. I'm impressed with your level of honesty in looking at yourself and think it's probably a sign of being a very good parent.
