If you're working on a team it's a plus (well can be good or bad sometime), usually in organisations the team as a whole is responsible. So I think from your manager's response, she's not concerned about you. But honestly, If you have issues taking huge responsibility, it could be from many reasons. I suggest that you honestly sit with yourself and know your skills and what's lacking (ie. what are you not so good at?) Perhaps you're afraid of taking tasks that you're not occupied with the skills to fulfil them or someone's is doing better/faster/more efficient...etc. I'm sure everyone's skilled in some way or the other.

Just discover and uncover your talents & skills, you'll be amazed by your capabilities!

For fun: For you, I find this quiz a cool fun way to start -- it's called "Test your skills with MindTools" google it!
Ps Plz don't take it seriously, just one of these fun online quizzes.