There is a difference between being introverted and being shy. I was painfully shy and very quiet for many years. I have learned to talk and now am at the other extreme!

I think, as the others said, that people misinterpret shyness as rejection of them. Maybe smiling and at least nodding and making noises like "That's nice" and showing more obvious interest but not having to talk much would help. Is there someone you trust you can practice with?