I don't think that this is important.
You were using the Console App, clicked logs, and then deleted the Console.log. Or am I wrong?
It should rebuild it's self. If you clicked Clear Log you just deleted the entries that were logged, and nothing bad should happen. Unless your working with an AppleCare tech. They may require those logs, but I can't see why.
If you were using the Terminal, did you use the rm command, and what permissions were you using?