You sound like you're more focused on yourself during the interaction than in them. You can be an introvert, but that doesn't mean introverts can't relate to people. Introverts just mean that you recharge your batteries by being alone at the end of the day whereas extroverts recharge their batteries by being around other people. But being introspective (ie looking inwards at yourself) means you're not focused on the girl and how you can make her feel good and bless her in some way.
If you go into an interaction constantly thinking "what will they think of me?" or "don't creep her out" then even if she is initially relating to you normally, she'll sense that your head is somewhere else and you're not even concentrating on her, and that can put her off. She may not necessarily be creeped out (that could be your perception of things). It may be that she simply thinks you're not interested in her as a person (because you're actually thinking about yourself in that moment).
When women sometimes gesture that their eyes are here by pointing to their eyes and not to their boobs, you need to apply some of that to yourself. Don't focus on your OWN chest area, metaphorically speaking, but look into her eyes instead - ie don't look inwards but outwards at her. I know that sometimes is easier said than done, but if you're focusing on yourself, you're in the wrong head space to be relating to her, and she'll sense that, and then you're not engaged in the conversation and that will put her off (which you'll then perceive as having creeped her out).