As played, fold on the river.

If you think you are best on the turn you should bet there, as if he doesn't have a straight and is on say, a diamond draw he is freerolling so I suppose you thought you were trailing, or (less likely) so far ahead he was drawing dead and any bet would scare him. I would need to be very sure of the latter read to feel great allowing the freeroll possibility, and I'm not sure I'd have ruled out his having a K. He may have felt the same way about your hand if he hit the straight!

I'd check turn and fold river...