Ivy is almost impossible to remove. There are a few ways to deal with Ivy . . .
The easiest way for you, since you have already dug out and removed a lot of Ivy roots, is to just keep careful watch for any Ivy foliage that has started to grow back in the area you don't want it in and remove it.
Other plants can grow around the Ivy roots if the growth of the Ivy is kept in check. Choose plants that can grow with shallow root systems, like Impatiens and Moss Roses.
Another way is to spray herbicide directly on the Ivy roots. You would have to be very careful not to allow the herbicide to touch the roots of any plants you want to keep. Herbicides only last for a short time so you would have to keep spraying the Ivy roots every few weeks. This may or may not interfere with you growing other plants in that area, depending on the specific plants you want to grow there.
Finally, you can cover the area with about 6 or 7 inches of mulch. The mulch will block the sunlight and prevent the Ivy from growing back. However, it will also keep any other plants from growing there too. I have used mulch to keep Ivy from growing in places that I didn't want it to and then just not put down mulch in the places I wanted to allow Ivy to grow.