My 3-1/2-year-old has lately been saying things that are the opposite of what he means. He'll say he doesn't like something or doesn't want to do something that I know he does. He's also occasionally said "I don't love you" or "I don't like you" when we're saying goodnight. I usually just say I love him but that if he doesn't want me around right now, then I will leave. He changes his tune immediately and says he does love me and wants me to come back in the room. I think this is an age when kids experiment with saying things that they don't understand or that aren't true. I think you responded in exactly the right way.
I imagine that kids can come up with this sort of thing on their own. Using the word "hate" is obviously different, so I agree with others that you should ask your daughter where she heard a word like that.
In terms of a response, I think it's really important that kids feel like they are allowed to express their feelings. So even though your daughter probably wasn't actually trying to express a feeling but just trying to test out some new language, I'd still be careful about trying to punish it in any way. When my son says something hurtful (especially if he is in fact trying to express his displeasure at his brother for taking a toy or at me for disciplining him), I tell him it's ok to be mad/sad/hurt etc. and that it's ok to say how he feels, but it isn't ok to say mean things about other people. I offer him an alternative way to express his feelings. For example, if he were to way "I hate you" because he got put in time out, I'd tell him he could say "I'm mad at you because _____" instead. This probably isn't an appropriate response in the situation you described (because your daughter probably wasn't actually mad), but nonetheless it might be good to keep in mind that kids need help figuring out how to say what they are feeling and that you don't want to give your daughter the impression that she might be punished if she says the wrong thing (when she gets older, though, I can see that there could be some language that might merit punishment).