It is very tough for uni graduates these days. Some students do get lucky and do internships and then get offered permanent roles after, but that's not the case for a lot of people. It is incredibly tough competition and it is important for you to have high self-esteem and lots of confidence throughout the recruitment process and to have a good ability to pass interviews and psychometric tests. I am a graduate myself and I am warning you that competition is tough. Do not expect to finish uni and walk into a job, because employers don't give a crap about which uni you went to. All they want is to see your transferable skills, so for example, being a good team player, working well under pressure, being organised and someone who takes initiative.
And there are thousands of graduates who are searching for jobs. It doesn't matter if you apply for a small company, a medium-sized company or a large company. Every single job role that I have looked at had at least 30 other applicants. Some roles have 50, 100 or even 200 people applying for the same role! That's insane. It's very very hard to stand out and there's no guarantee that you'll beat the competition, so to answer your question, yes it is very depressing because you start to understand that you are almost insignificant to these recruiters if they have so many candidates.