1点差で負けたので、悔しくてならない。- Expressing a feeling or state of emotion that is the natural outcome of a situation beyond the control of the speaker. EMOTION, FEELINGS, DESIRE are needed. "I'm so regretful that losing by one point." Old-fashioned, used in written language.
1点差で負けたので、悔しくてしょうがない。 Expressing a feeling or state of emotion that is the natural outcome of a situation beyond the control of the speaker. EMOTION, FEELINGS, DESIRE are not necessarily needed. It can be a situation that lies outside the speaker's control, not related to emotion (a baby crying, someone sassing back) that results in annoyance, etc.. ~仕方がない is often used in writing. "I'm so heartbroken that they lost buy one point that I don't know what to do." (possible translation)
1点差で負けたので、悔しくてたまらない。 A strong feeling, sensation or want on the part of the speaker. "I'm so disappointed we lost by one point that I just can't stand it."