ideally they should have gone straight into the soil. The roots that will become the carrot dont like disturbance.

Yes, rootcrops generally should be sown direct into the ground as Sbg says and thinned when nessesary. The tap root will probably not grow properly either.

Carrots are also especially susceptible to carrot root fly. This insects maggots burrow into the tap root completely ruining it. Any disturbance ie. planting out will inevitably release the smell that attracts these flies.

Personally I'd chuck the ones you have in the propagator and start again sown where they are to grow. Make sure you have a fine tilth and do not add any compost to the soil as it will encourage the root to fork. Keep them covered or the root fly will be along and lay its eggs in them. Unless your soil temperature is over 4˚ I'd hold off on sowing yet.