A specific word for "oblivious to love"

Clueless is a term clearly broader in use than any romantic situation, but it certainly captures the way I felt when I was that guy.

completely or hopelessly bewildered, unaware, ignorant, or foolish

Perhaps blind to love.

Example from the lyrics of "The Lizzie McGuire Movie":

You've been searching the world to find true love
Looking in all the wrong places
When all of the time you've been blind to love
As plain as the nose on your faces

Usually, such people are referred to as naive, or unsophisticated. Since you are probably looking for a more endearing term, you might consider:

• unassuming: not having or showing a desire to be noticed, praised, etc.

If you don't mind using a slangy term:

• adorkable: Adorable in a dorky, socially awkward manner.