EXCLUSIVERobin Thicke is so desperate to get his wife back ... he WROTE A NEW SONG about it -- including the lyrics "I should've kissed you longer / I should've held you stronger" -- and TMZ has learned he'll debut it live on stage ... at the Billboard Music Awards.
TMZ has obtained a copy of the lyrics for the new song -- called "Get Her Back" -- and the whole thing is dripping with regret over his split from Paula Patton.
-- "All I wanna do is make it right"
-- "I gotta get her, go get her back / I gotta treat her right / I gotta cherish her for life"
-- "I should've kissed you longer / I should've held you stronger / And I'll wait for forever for you."
Robin's other public pleas to Paula -- opening up during concerts about forgiveness -- have fallen on deaf ears.
If at first you don't succeed ... beg in front of a national TV audience Sunday night at 8:00 PM on ABC.