Growing grass in seed tray

What you could try that worked well for us is to pre-germinate the grass seed.

Get a clear polythene sealable bag, add approx two parts, by volume, of compost or fine soil, with one part of grass seed, mix well and the add just a little water to slightly moisten the mix.
Leave it somewhere warm and light and check closely every day for signs of the very fine roots appearing on the seeds.
You can turn the mix over each days well so you get and even germination.

One you see those fine whte roots thats the time to spread the mix onto the area you want to patch.
Just cover with a bit of netting held up with a stick to stop the birds, and it should continue to grow ok.