You should not have let them go to stalk. That is called bolting. It reduces the longevity of the perennial chicory in the plot and reduces the amount of forage produced from the plot. Chicory should be kept at a height of no more than 10 to 12 iches to prevent bolting.
I would mow it and save what you can ,.. then overseed it again in the fall. Mix in alittle red clover also. Works great..