Dentist left part of my tooth exposed with new crown, are they responsible to replace it?

Hello there, I advice to communicate directly with the Doctor who performed the dental work, express how you feel and the symptoms you are having, sometimes we leave a portion of the tooth for other reasons, or to prevent damaging the tooth structure with the preparations, there are many factors in consideration, but definitely try to address your concern and let them know you are feeling sensitivity. I can speculate about what could happened since I don't have any photos before and after, but I am sure they will find a solution for your concern.