But panick? not unless you live in the UK. I'd expect mainland EU to continue almost as usual, with maybe a few high-energy factories shutting down. But since most of the jobs are service sector anyway, I wouldn't worry too much.
I heard the news that in Germany a car part supplier started bankruptcy proceedings. But that's only 2000 jobs out of 84 million people. And all those coal and steel factories were only very few jobs, too.