Found an error in my published conference paper
The reality is that the best answer is simply "get used to it". It is sad that this happened to you in your first conference paper, but things do get published with mistakes, and there is really nothing very much anyone can do about: you can proof read papers as often as you want, and there will always be mistakes. I'm not saying this because I am a nihilist but simply because I'm pragmatic: of course I want papers to be perfect; it just isn't practical.

The interesting question is only: how severe is the error. You don't answer this in your question above, but if it is really only a typo or misspelling, then it would not be worth your sleep. If it is a mistake that a reasonably educated reader will be able to understand as a mistake, the same would probably apply. If you submitted a proof that has a mistake and upon further thought you realize that the whole theorem is not true, that would be a separate matter -- but you wouldn't introduce such an error while dealing with the final version of the paper.