did you put slug pellets down, because it sounds like the slimy creatures.
Definitely a strong likelihood as tiny ones eat the germinating seedlings before they put their heads up above the soil surface. Adding some pellets in the row as you sow, as well as a very thin scattering along the surface of the soil around the drill might help. There are some available which are not so damaging to other wildlife
The other possibility is that the soil,, despite your care, is too dry. Try soaking the drill well an hour before sowing... really, really well, not just a dribble, and then lightly water the compost you put to line the drill before sowing. Cover carefully but also add a thin layer of dry soil as this acts as a barrier against evaporation. Press down gently all along the drill with the palm of your hand to make sure the seeds are in good contact with the damp soil
If there is no rain, for a couple of days, water the soil alongside the drill, not directly on it, both sides. The reason for this is that as wet soil dries, it can form a hard layer (called capping) and seedlings may not be able to push their way through it.
If the weather is scorching hot and you can't dey sowing until it is cooler, shade the soil surface with something like a double layer of debris netting
I hope that helps
And no, it is not too late for either carrots or beetroot to be sown