It's a common issue with being shy, that people think you are unable to do a task well ( e.g. perform on stage) because they see you as quiet and shy.
1-SHOW THEM YOU CAN-
Do the task anyway the best you can do it.
Be brave and work hard to proof them wrong.
2-DON'T BACK OUT/DOWN-
Just because people say no to you doing it or think you'd suck...don't let that put up a barrier.
Some shy people go into a bubble and hide away when people out shine them. Try and pop the bubble by pushing yourself into activities.
3-TURN NEGATIVE INTO POSITIVE-
Tell yourself "yes I can" when someone says you can't as your too shy. Every mean comment or expression given is a chance to make it into opposite reactions.
4-DON'T TALK BACK ABOUT IT-
Calmly go about your day doing thing you're underestimated for. Don't speak out and say "I think you'll find I can do that" ...simple go and do the thing. Actions speak louder than words plus don't want to be laughed at for speaking up when shy people find speaking out hard.
5-SET YOURSELF TARGETS-
Give yourself an achievable goal to get to. If someone says you can't join the debate team because you're too shy or be a leader of a group...then show them ways you can talk out.
Volunteer for activities that involve a good portion of it talking...e.g. in charity shop or handing out leaflets. (run for class president etc).
Never give up and take easy way out. Quitting means the underestimater wins and is right.
Get a friend to help you get better at the task you're underestimated for...or just to give you positive reinforcement to keep going...e.g. positive comment or give you a cookie when done well.
Do what you feel makes you happy. If you end up in tears then it's not right for you. Try enough to show the person you can succeed but not so you become sad by it.
Stay happy and show the person who belittled you that their comment isn't getting to you and you aren't affected by it...even though you are inside. Your face should show you're happy, some people only wish to troll you and make you suffer for their happiness as shy people tend to be easy targets.