You could try protecting the "good" grass surrounding the clumps by wrappinig some plastic around the base of the stuff you're trying to kill and then spraying it. With Glyphosate all you need to do is mist down the foliage which will then carry the herbicide to the roots and kill it. I've found mixing in a little dish detergent with the glyphosate helps it stick to the leaves better. You're still going to end up with a bare spot where the weed was. When did you reseed the lawn (time of year)? And what type of seed did you put out?

Carefully cut them down and immediately paint the stump with RoundUp. It will resprout, but either brake the sprouts off or spray them with RoundUp. Suckers will also come up from the roots, but keep mowing them. Eventually, without leaves for photosynthesis, all will die. But it is an ongoing battle for a while.I usually never use Roundup, but do for locust and Johnson grass & poison ivy. (I am allergic to locust thorns and poison ivy, and you never get all of the roots of Johnson grass the first time.)

In your photo there are LOTS of little seedlings, which means there must have been lots of seeds in your lawn or in the compost you put down. You didn't mention the lawn having lots of weeds previously so I wonder about the compost. Where did it come from? Your options are limited while the new grass is just getting started since many broadleaf herbicides can damage the grass seedlings too. If you wait until the grass is established at least 8 weeks, then you may be able to use herbicides. Check the label of any product before using it on new lawns. I agree with kimmsr that correcting soil problems is the way to manage moss in a lawn. Moss is not a competitive plant, as you can see by the very limited root system it has. It grows in lawns where the grass is already doing poorly. This can be cause by lack of soil fertility (the most common cause in my experience), too much shade, heavy soils that drain poorly, and excess acidity (pH below about 5.2). Lack of organic matter isn't normally limiting for grass, but adding organic matter can improve drainage if that is the problem. Have you had a soil test done? You mention that the soil was determined to be acidic. What was the pH?

Another option is Gordon Ornamec 170, it's cheaper than 2 bottles of the Bayer and will last you many years. It's also good for other tough weeds like quackgrass and dallisgrass. https://www.amazon.com/Ornamec-170-Herbicide-32-oz/dp/B008MZQE6O/ref=sr_1_1?ie=UTF8&qid=1470488280&sr=8-1&keywords=ornamec+170 Yes, you will need to apply a pre-emergent. I recommend prodiamine, it will control this and most other weeds.