As carrots lose leaf area to blights, the plants are weakened and may not reach full size. Frequently the weakened carrot stems will break off when you try to pull a plant from the ground, so carrots must be dug rather than pulled when they are ready to harvest.
Always rotate crops, and thin carrots to proper spacing so they will get plenty of sun and fresh air. No carrot varieties are truly resistant to this disease, but some are more susceptible than others. Observe varietal differences in your garden, and replant varieties that show little or no spotting of leaves.
Clip off blighted leaves, and pull any weeds that may be encouraging dank conditions. Dig and store carrots as soon as they are ready.