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 
Bill says
Think I may have gone about the sucker removal all wrong. I used a propane burner to burn down the sucker hedge that has grown up inside the brick wall perimeter around my Oak tree. I have noticed some browning of the leaves on the tree. Hopefully just a shock and it will green back up in a week or so.
james says
Hopefully. I had never thought of that idea, would be a little afraid of trying it. But sometimes a plant problem will make you so mad, you will try anything. Please let me know if this works out for you, and I will pass it along.
Ian says
Bill – do you have any updates on your torching approach? I hoped this would be the silver bullet… since i don’t like any of the other options :). Great blog, though. I appreciated reading through everyone’s ideas and James’ original post. Stay vigilant with those suckers!
Reagan says
I have to watch them with a pair burner they still come back
Gery says
Has anyone put artificial grass over the sapling affect area?
james says
I never heard of anyone trying that, Gery. It might work. The matrix of the artificial grass might hold the suckers back, or you might need another layer under it of heavier construction geotextile. But artificial turf is usually put atop a base of crushed stone or similar, I worry that the extra layer of base material might cause problems for the tree.