Yes, what you said could have been interpreted as "I'm not really interested so don't think I am." So now you need to show her you are interested, that's all. Depending on the level of discussion you've already had relationship-wise, I might hesitate to give her the "respecting her privacy speech" although it was a lot better then what you did say.
It seems that this might just escalate the awkwardness of it all right now, so instead just make the next move, be attentive, laugh at her jokes (hopefully, don't be fake though) and let nature take its course. She may be a little edgy because she's kind of putting herself out there and taking a little risk by showing so much interest, so she's in a vulnerable spot. If it's reciprocated, she'll forget about the awkwardness and you guys can talk it over later after the next level of intimacy has been established.