fescue will grow faster but if youre throwing new seed on you have to water it everyday, like soak that bitch until it sprouts.
since you got new sod, you really don't have to worry about thatch, so all you have to do is throw some seed on
i personally use scotts cuz i had goodluck w/ it in ks and i got the "southern gold" mix for tn and it works well, also it's blue so i can see it when i throw it
so just throw some seed on the dead area, (like make it all blue, just b/c you have a little bit of seed there, doesn't mean it'll grow) maybe clear away some dead grass first, then throw a sprinkling of top soil/compost (i prefer compost) until you don't see the blue anymore (this covers the seed and prevents birds from eating your seed).
i top it off with a sprinkling of milorganite, i recommend you use this as your first form of fertilizer b/c it's organic. (not for fu fu save the earth reasons, but b/c it's organic you really can't put too much or too little and end up killing the area as opposed to syntehtic ferts)
if you forget where your dead grass is, get some flags and just pop em in to remind yourself
you'll have other uses for them i'm sure, it's easy to get lost in the lawn after a while.