I never feel proud of my accomplishments

I've realized lately that I'm never really happy when I accomplish anything, whether it's something big or small. I always feel like I got lucky, or that I shouldn't be proud because I just barely managed it, etc.

I just got into a very competitive graduate program. I've wanted this more than anything in the world for years and I was convinced I'd never achieve it because I couldn't get my life together. I should be over the moon right now, but I just feel like I lucked into this and didn't actually work hard enough to deserve it. I don't think it's just typical impostor syndrome because I know I'd feel the same way if it was something minor.

Does anyone else have this problem? How do you deal with it?