How very frustrating! So sorry to hear that didn't work out. However, I don't think you should be embarrassed. After all, knowledge in a particular field does not automatically mean you know how to do everything in that field, right? And we all try things that just don't work sometimes. There's no shame in that; it's just part of the learning experience (I think of it as an important part of creativity--the try-it-until-you-get-it-right kind).
Can you take the lining out and leave the mittens as they were originally? And can you make larger mittens and reuse the lining in those?