I have been on Student Visa (F-1) for 4 years. I've done my taxes returns with the 1040NR-EZ form but didn't know I was supposed to attach Form 8843. Can I just send IRS Form 8843 for these 4 years now?

No need to send Form 8843 now. IRS has been processing your return without Form 8843.

In this case, I disagree with MukatA.

Download the Forms 8843 for each year not filed from www.irs.gov and submit them late. The Form 8843 is used to validate your F-1 visa status, and submission of the form, even late, allows you to maintain that status.