Firstly (probably this is an innocent mistake), you need the pronoun I at the start of the sentence, rather than it.
As for your main question, the difference is minor really, but there is one.
You might use needn't if the film that you wanted to watch was also on the TV.
I needn't have done sth, because *outcome* (there was no need to carry out a particular action, as the outcome was the same anyway = if I went to the movies, or if I stayed home, I saw what I wanted to see).
Shouldn't usually implies a prohibition of something. You shouldn't talk in class/chew gum/steal things etc.
In your case, shouldn't implies that it was a bad idea to have done something. "I shouldn't have gone to the movies (because it is expensive), I could have seen something on TV (it is much cheaper to stay home).
Those are the technical differences in your sentences. However, realistically, you could use either to express the point you wish to make.