Don't forget, if you had set your sights on getting an internship with Google/Microsoft there was a significant chance you'd have failed to get the internship there too if they preferred others' cover letters or had met their quota by the time they saw your application. Just as with paid work, they're not short of applicants.

Good news is, they need the full time employees more, they won't care at all about internships when you've got valuable real-life experience, and you get a lot of opportunities to reapply to companies that size in future.