We have all had that feeling at one point in our lives and it usually affects us negatively sometimes even catastrophically. But when it happens in the work place it has an entirely new affect on us. It not only makes you feel like you can not do the job properly but it also makes you feel discouraged to try again in that particular field. The feeling of not good enough is enough to over power even the most confident of people.
You start to doubt yourself, who you are and what you do, your ability, the time you have spent learning and maybe even question if you made the right choice in career. As hard as it is, do NOT give in or give up. Keep pushing through the No's until you get to the Yes. Sometimes no matter how hard you work or how much you put into something, it is just never going to be enough for someone but there WILL be someone out there who it WILL be enough for. You just have to keep going until you find that person/place.
One of my favorite quotes is "The only person who can keep you down is yourself" and it is so true, only you stand in your own way of happiness with these feelings of doubt and worthlessness. It is only in your mind that these things can become true. Don't let them win, USE IT. Use it as the force behind you to keep you going and prove them wrong.