The atomic bomb didn't single-handedly bring Japan to its knees. The failed negotiations with the Soviets and the invasion of Manchuria had at least as much if not more to do with that. I know people like to think "the bomb won the war period" because that way no one has to feel bad about it anymore but it's not so easy.
It was the final nail in the coffin which brought Japan to realize it was better to end the war with out more blood spilled.
I for one do not feel bad about it. I think most people don't either. Hell I agree with the bombings.