In this situation you should use "I haven't seen it yet" the present perfect version. This is because the present perfect tense relates to "unfinished" time, thus indicating that you will see "it" sometime in the near future. Also the word "yet" is very commonly used with the present perfect tense and not the past simple version "I didn't see it yet."

did is past tense and when you say yet its present tense , and 'Yet' implies continuation and its used to talk about something which is expected to happen. It means ‘at any time up to now’. also It is used in questions and negatives. , I haven't seen it yet means -----: I have not seen this thing but there is a possibility to see it , you still be able to see that thing , its what we call " present perfect " Example : Paul has broken the vase another example : Dad hasn’t washed up yet !! but there is still a posibility to do that . it's implied that there's still an opportunity for you to "see" whatever there is to see the first is simple past ( i did not see ) : i think you know the difference now