It's normal to think it, but you shouldn't let this define who you are as a person. If you let every thought get to you, you'll run yourself dry. You are you, and you are beautiful just the way you are. If it's something like a sport, remember why you began playing it in the first place.
I think everyone goes through these kinds of feelings, even if they don't suffer from anxiety or depression. Especially during times of stress, or changes. It may still be helpful to look up different resources for handling anxiety when you're feeling this way. Just because you don't need them on the regular doesn't mean they can't be helpful. And if you're noticing these feelings more frequently, and you're having a hard time on a day to day basis, it's worth bringing up to your doctor.
I think it's definitely normal. A lot of times we look to others and see how well they are doing, how popular they might be and how easy it seems for them - looking around, we don't catch sight of anyone asking the teacher too many questions or appearing to lag behind, and automatically we start thinking we're the ones who are behind. However, it doesn't mean you're not doing great at that one something! You have your own individual talent that you bring to the table, that no one else will quite be able to offer, and you should always try your best to use that to your potential!
It's normal for anyone to feel inadequate at times, and it will help to talk about it to a trusted friend or get support with a mentor or someone in your grade, if this is a school setting.
Depression is a tricky thing though. Lots of people suffer from it, but don't know. Depression also varies. You can be mildly depressed and everything above. You might just have low confidence at times that cause you to feel this way.