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.
Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.
For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.
Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).