Sample size for a survey is based on accuracy not generalizability. The fact that you have fewer responses than expected therefore decreases the accuracy of your prevalence estimates, not the generalizability.
To assess generalizability, compare the demographics of your sample with that of the target population.
The generalisability of your findings also depends upon the probability value of your test. If the test yields very strong evidence to reject H0 then the results are of value to the population even if the sample size was not adequate for ensuring a sufficient test power.