I recently experienced something similar. I had to tell a client I was in over my head on a project and it felt absolutely awful. I'm not one to give up so this went against everything in my body. I was also concerned about how this would look professionally.

However, the next day (and for almost a week later) I received many emails asking for services and pricing. And the client totally understood and still wants me to do other work! Definitely proof that when one door closes, another opens.