Unfortunately, your body language probably said "not interested," and some women pay more attention to that than to what might be said afterwards.
Personally, I would prefer it if a guy said "yes, I'm interested, I'm just not expressing myself very well." Of course, maybe that's just me, but I don't think it could hurt.
Be up front verbally. If you're uncomfortable with eye contact, tell her that you're "shy" (that's always a good word to use), but you are still interested in a date and would like to get to know her better.
If that doesn't work right away, I agree with Lene and MissConstrue to "be patient"--a girl will come along who will respond to sincerity.
Don't give up.
Who knows you might eventually find yourself just as successful as Genghis Khan.