There are almost never seedlings growing from acorns. If there were, you would be able to pull them up easily. What you see are sprouts from the roots of the existing tree; therefore, you do not want to spray a herbicide on them in an attempt to eliminate the sprouts for you will hurt the “mother” tree along with the sprouts.
Only a small percentage of oaks send up suckers from the roots. It is a genetic trait, like freckles, except I like freckles. But like freckles and sunshine, some trees have the ability to sucker, but do not unless stimulated to do so. Oaks having a slight tendency to sprout suckers will often do so when roots hit a barrier, such as trees confined to a parking lot planter, or between a sidewalk and driveway. Also, when roots are disturbed and damaged by rototilling, they are more likely to sprout suckers. But some trees never will make suckers. When choosing an oak in a garden center, if there are sprouts coming up at the inside edges of the container, I would avoid that tree.
You may choose to mow them along with the grass, if grass still exists. Or if the grass has thinned too much, you might plant Asiatic Jasmine groundcover, and use hedge trimmers to trim the jasmine and oak sprouts to a uniform height. You can cover the area of sprouts with a heavy gauge woven geotextile, and then either mulch or spread large gravel or decomposed granite over the top of the geotextile. My favorite solution, when appropriate, is to cover the ground with geotextile and then build a wood deck.
Or if you prefer a thick green lawn, you may remove the oak tree, and all of the tree roots with a backhoe. If you just cut down the tree, grind down the stump and all the large roots you can see, there will still be thousands of oak sprouts emerging from the remaining roots in your new lawn or bed area for a few years afterwards. The area will need to be continually sprayed with an herbicide.
James 
Linda says
We moved here (Swinney Switch) 25 yeas ago with a little better than 1 1/2 acres with much johnson grass. Regular mowing keeps it in check in our yard but it is a major pain in our vegetable garden. Is there a solution other than digging to China to remove this. I won’t use harmful chemicals and spraying with vinegar seems too difficult because of the closeness of the veggies. Can you help. We have raised beds and johnson grass grows from the paths into the raised beds via the underground roots, tubers, or what ever you call these evil things.
James Gill says
I suggest you dig to China (no, just 18″-24″) and put in a plastic rhizome barrier around each raised planter. Then stay busy digging every rhizome inside each planter until you have got them all.
Virginia Hoff says
What a great discussion. I am in New Orleans with a big 100 year old live oak in my backyard adjoining an area of sun with grass. There’s a block fence, running the length of the yard along its back perimeter and this is where the suckers sprout. I put elderberry, beauty berry, titi and similar native shrubs among the suckers and a couple of hammocks strategically placed. An arborist thins and trims the oak every 2 years. On the non-sucker side I put native shade forbs & ground covers. Altogether it’s actually gorgeous. When a sucker gets 4’ high is when I cut it back. It works for me. Plus I like the birds, squirrels and butterflies that come around.