It's difficult to say without knowing more about the exam itself. Assuming that there wasn't a time limit set to kick you out, it could have been that your clock was off a little bit from the system. Or you may have pressed Submit with 5 seconds left but due to network congestion, etc it took more than 5 seconds for the submission to fully take place and thus marked it a minute late.
Talk to your instructor and let them know you thought you had clicked Submit within the time window and don't know why it says 1 minute late. I'm hopeful your instructor will understand that sometimes things take many seconds to fully submit which could account for the 1 minute lateness.