NO! Even if you didn’t cause the accident, don’t say anything that sounds like you are admitting fault.
Spontaneous (res gestae) statements in emergencies or stressful situations often hold up as truth during legal proceedings.
Don’t say, “it’s my fault.” Fault is a legal issue that insurers, attorneys, and courts decide. If you admit fault, your words influence claim outcomes, especially in the face of conflicting versions and inconclusive physical evidence.
Don’t apologize or say “I’m sorry.” Sometimes nice people apologize because that is just who they are, but it sounds like you are admitting fault.
Do help injured people, but don’t say you are sorry. It sounds like you believe you caused their injuries.