We're also wondering what could have caused this kind of damage. Marilou, Right now is the best time to repair these areas and get the grass established for a good growing season. It certainly can be done now especially if it stays cool a little longer. And you MUST keep it moist until all the seed has germinated and then keep watered all summer. It is more expensive but may be ok for a small area.
Good preparation is essential.
Remove dead turf or till it under well, add some brown dirt, fertilize and mix into soil lightly, then lay sod. Make a smooth seedbed, fertilize and work in lightly. Apply seed evenly, tamp to assure good contact and lightly straw to help hold in moisture. Water 1 - 2 times daily for 2 full weeks. As to what caused the problem - necrotic ring spot is a pretty common turf disease that seems to come and go in many lawns.