disadvantages of FFT, it can not extract enough frequencies without enough samples
Any measurement has a finite precision. You can't find real frequency exactly in general. You can evaluate it with necessary precision instead. In the case of FFT if the real frequency doesn't match FFT frequency grid exactly, power spectrum is spreading mostly among neighbouring frequency bins (among all bins in general, but most of it is focused in a few adjacent ones). Nevertheless you can estimate the real frequency by finding maximum of such a spectrum. Dealing with FFT you can improve the precision of frequency search by increasing the number of samples. If you can't, you should use another power spectrum estimation techniques but it's the separate question.

Hope this helps.