C.K.
Do you notice if she's spitting up more after certain foods? Have you introduced any dairy yet? Spitting up a lot at that age may be more of a food sensitivity than an issue with the cup. Kids are still sometimes pretty sensitive to dairy products at 11 months, so if you've tried introducing some diary, it could be that. You should talk to your pediatrician about it.
If it is the cup and she's sucking in too much air, I'd suggest waiting a couple of months and re-introducing it. Maybe she's just not quite ready.