Answer: What you describe sounds like pearlwort, a weed rather than moss or algae. It is low growing and green but the flowers turn into orange colored seed pods. It is creeping and grows best when lawns are mowed short. You can dig/pull the weeds out or use a broadleaf weed killer containing 2,4-D which won't harm your lawn but will kill the pearlwort. You may have to make repeat applications because the seeds from previous plants may still sprout. Here's a link to a few photos of pearlwort: http://www.ipm.ucdavis.edu/PMG/WEEDS/birdseye_pearlwort.html
Clicking on either photo will enlarge it enough for you to see the growth pattern and seed pods.
Best wishes with your lawn.
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