You have 3 choices here: (1) like, (2) that, (3) as if.
It's not like I didn't want to talk to her. Here I am denying the idea that I didn't want to talk to her; I'm saying that the opposite is true. See here for more examples. As noted in the comments, this usage is the more informal version of the next example.
It's not as if I didn't want to talk to her. Collins gives this definition and example:
You use 'It's not as if' to introduce a statement which, if it were true, might explain something puzzling, although in fact it is not true.
I am surprised by the fuss she's making. It's not as if my personality has changed.
It's not that I didn't want to talk to her. The purpose of this sentence is to deny something that appears to be true by giving an alternative explanation of the facts. It's not that I didn't want to talk to her. It's just that I get really nervous talking to pretty women. If you say "It's not that...", I would expect a second statement explaining how it actually is. See here for a good explanation on another SE site.
In summary, all three expressions are valid and they are all similar but with subtle variations. Welcome to the English language!