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 
Rosemary Willfong Willfong-Turpin says
People who come in on this web site trying to sell something and leaving their advice for how the web site’s experts handle things, ought not to be so rude!!! Please stop and refrain from interfering in what this site was intended for. We come in for here advice, and we are not here to be sold on some other product from rude and nasty opportunists!
Suzanne says
Never say never! : > ) After an unusually wet spring and early summer many lawns in KC – including ours – are filled with the small seedlings from sprouted acorns. We know it’s acorns and not sprouts from the tree roots because when pulled every little seedling root has an acorn attached to it! Several shorter than usual mowings have not done them in – they just continue to leaf out again in a day or so. Hardy and persistent little guys! : > ( Considering attacking them by hand, but oh the hours it would take. Any other alternative?
james gill says
Suzanne, I’m at a loss for solutions. A broadleaf weed killer such a Triclopyr will kill oak seedlings without harming the grass, but a spray application will definately damage or even kill the main tree. Roundup will kill the seedlings AND the lawn without harming the main tree, if they are indeed seedlings and not suckers. Using a wiper application of Triclopyr with NO spillage of chemical might be successful, but is risky. So I can’t wholeheartedly recommend any of these. You could attempt covering with old carpet or refrigerator boxes to suffocate the seedlings, being sure you still apply adequate water to the roots of the main tree. Best of luck.