The grime you see on your collar is not dirt, it's actually a build-up of sweat along with the oils from your skin. That's why normal washing rarely removes it.
Toss the shirt in the regular laundry and it should come out good as new.
Prevent future rings by washing your light colored shirts after every wearing. Run a gel stain remover, like Shout Ultra Concentrated Gel ($3.50 at Drugstore.com) before washing.