you don’t know the pasteurized milk? Pasteurization is heating for very short time.It should kill bacteria, but not spores and probably also shouldn’t destroy some nutrients

Pasteurization is at lower temperature and short time. Have look at the mighty Wikipedia for the details. It is probably because your medium will form some precipitate if heated at the temperature used for autoclaving. I know Instant Ocean (one brand of artificial seawater) does.
Alternatively you could try microfiltration (that is what I use for Instant Ocean) with a 0.22µm or 0.45µm filter.

hi
Pasteurization is only a method of reducing the microbial load in the given material. it differs from sterilization which is the process of making the material free from all forms of life. Pasteurization aims at killing pathogens and most of the vegetative forms of life. sterility is not assured. After pasteurization your medium will be only "disinfected" but not sterilized. many media are unfavorable for the growth of ordinary contaminants and hence mere pasteurization is sufficient. there is no need to actually sterilize (autoclave) sea water medium as it already poses challenge for the propagation of common micoorganisms. morreover, attempts to sterilize sea water could end up leaving behind cloudy precipitates in the medium..

if you still insist on having a sterile medium only, then you must go in for filtration method of sterilization.

Disinfection is an entirely diferent concept versus pasteurization.