Yes. Two conditions must be met before police are required to inform you of your rights per Miranda.... 1. You must be in custody (or otherwise detained and not free to leave) and 2. They believe you to be the suspect of a crime and are asking you questions about that crime.
When an officer questions you at the scene of an incident, you are not in custody and not necessarily detained... and since you are still at the scene it is unlikely that the officer has enough information to suspect you of a crime, so his asking you what happened is not unlawful.
However, once he zeros in on you as a suspect, and you are told you are not free to go, then Miranda becomes an issue.
Anyway... as you asked the question, the answer is yes, the conversation is admissible if the officer should put it into his report. There might be other details that effect this though. If you were handcuffed in the back of a police car and asked about something that just went down, then there might be some kind of violation.