I remember reading a short story a few years ago about a starship crew from Earth(?), in either their first (or a new model) FTL ship. The story opened with them in a new star system, which they had surveyed and were now preparing to leave. They duly fired up their engines and departed in FTL mode.
Later they scanned the system they'd left, only to find that its star had gone nova/supernova. After checking timings, they realised that the star had exploded at exactly the same time as they'd turned on their FTL drive. After that, it began to dawn on them they'd not looked back at Earth after leaving it using their FTL mode... Oops. The story ended with them waiting for the light from Earth's sun to reach them.
I've bought quite a few older collections, and even more anthologies (as far back as Grof Conklin in the 1940s), so would hesitate to guess even a particular decade, but have the feeling it was written by someone like Arthur Clarke, Isaac Asimov, Harry Harrison etc.