Why are you afraid of her success? Is it jealousy or some other feeling based on comparisons with yourself? When you talk to other parents, is it based on the fear of exclusion from the group? Is it based on fear that you won't be able to provide for her needs if she is a star, or that she won't need you so much as a parent?
Is this really just a behavior pattern learned from your own parent(s)?
I'm mostly just tagging this thread out of interest, and I don't have any expert advice, but I think you're taking the first step by being self-aware. You could try making specific efforts, planned in advance, to say specific things to encourage your daughter. It might get easier as you go on.
Some of your comments may actually be having the effect of spurring your daughter on, if she wants to prove to you what she can do.
