The performance itself is immediately copyrighted the moment it's recorded.
If it's never recorded, then copyright doesn't really apply, as there's nothing to enforce.
The only thing that confuses people is who owns the copyright - that's the owner of the recording, which is not necessarily the same as the person who played it.
This even applies to a bootleg recording, which is where it gets tougher to enforce. Usually only the owner of the song copyright can bring a claim to court. Where this is a band or soloist playing their own material, the performance was at a ticketed concert, then the rule is clear. If the performance was impromptu or a cover, then it's generally harder to enforce.
Sometimes it comes down to the old adage "Possession is nine tenths of the law."
As far as I'm aware, US & EU laws on this are very similar, but if you need to fight it in court, don't ask the interwebz, ask a lawyer.