Concrete is not conducive to grass. It is hard, drains poorly and is highly alkaline. If you want grass to grow in an area where there was concrete, you must address several key issues. It's possible to grow grass where there was once concrete, however; and in time, with consistent care, the spot will be lush and green with lawn and no one will know that concrete ever touched the area.
Rake the surface of the soil with the garden rake. Lift out all the larger chunks of concrete if they haven't already been removed. Remove as much of the gravel as possible, as it will not contribute to a healthy lawn. Wear gloves when working with concrete, as it is rough on the skin.
Water the soil every few hours to prevent puddling so that the top six inches of the soil get moistened, especially if the area is extremely dry, as it tends to be after concrete has been in the area. Allow the site to drain so the soil is not too wet for tilling. If you can give it about 24 hours, it should be ready for the next step.
Rototill the area so that the ground is worked at least 6 inches down. It might be tough to get down through the top crust but after you have passed over it a couple of times, the soil should be pulverized enough. Do not try to till the ground if it is still too wet and clumping when you squeeze a handful of it, or you will be left with rock-hard chunks of soil when you are done.
Add 3 to 4 inches of compost and about 1 inch of peat moss over the top of the site. Pass over the area with the rototiller to mix the amendments into the soil. You should have a crumbly blend of soil, compost and peat moss.
Seed over the area with the appropriate kind of grass for the surroundings. In other words, if there is a lot of shade, plant a quick-growing shade grass. Some recommend planting a fine fescue like St. Augustine for shady lawns. A mix of Buffalo and Blue Grama has been recommended for sunny alkaline lawns.