Maybe I have been lucky, but I was in your same situation 3 months ago: 26, no job experience, soon to have a MSc degree in CS. I had your same fears when I published my resume on a portal that my uni makes available to students for making them in touch with companies, since then I've been contacted three times in the first two weeks and now that I found a job there are still other companies sending me emails offering me to have a job interview. The same thing happened to some of my friends.

Note that I was an average student, certainly not in the top of my course.