I finished my PhD at a time when the job market was very (very) unfavorable for mathematicians. It took years to recover. I had to keep lowering my expectations for a research job and eventually wound up in a very small teaching college. We did great work there with first generation college students from rural areas with modest qualifications, so it was, in itself rewarding. We boosted some people who needed boosting. (Note that this is a US focus.)
But just putting yourself out there with a CV, etc. isn't necessarily going to get you anywhere as everyone else is doing the same thing. Seek out a place that looks interesting and focus on it. More than one place, most likely.
The mistake I made was in not keeping abreast of the changes in the market and not keeping in contact with my advisor and other faculty members. I could have moved up sooner than I did and higher, but I was fairly satisfied, until I wasn't.
My advice is to find a position for which you are qualified (over qualified, perhaps) and will be satisfied in the short term even if it isn't your ideal, but keep an eye on the market and keep in contact with your circle of supporters. The market is bad now, as you have seen, but it can change. Use what resources you have to expand your circle, perhaps by attending meetings and conferences. You can also, if you are at a modest place, work to increase its impact, which I also had the chance to do. If you are able to increase the quality of the place you are at, and it is small-ish, it will likely reflect well on yourself.
For the purely emotional aspects, a professional can help. It would be devastating to fall into actual depression over this. It isn't you, necessarily, that is the source of the problem. Times are rough.