It's interesting really as to when you start classifying yourself as senior? I didn't really think too much about it when I started applying for roles as I had gained that confidence in my own ability.
That being said, I was almost put off working for one company because I thought at the time I might not be experienced enough. This turned out not to be the case at all and I'm so thankful I rode it out rather than letting my own self doubt influence my decision.
There are going to be companies out there with people in "senior" positions with less experience/skills and talent than you. In some cases considerably less. Don't sell yourself short because of a label you've given yourself.