From the context of the original Japanese text, is seems that しかたない does not imply a negative feeling such as disappointment or dissatisfaction. Instead, it seems to mean "That's just the way it is" without any negative connotations.
However, all the English translations I have found, such as...
- I can tolerate it
- I can live with it
- I can accept it
- Oh well...
do imply some degree of negative feeling. (One translation is "I don't like it, but I can live with it.")
The Wikipedia page https://en.wikipedia.org/wiki/Shikata_ga_nai is ambivalent about this question.
The context in which しかたない is being used is, for example:
- I have a headache.
- Here is a tablet. It takes 10 minutes to have an effect.
In English, that feels like (possibly slight) disappointment, but apparently, in Japanese, it does not.