I strain it through a towel before it goes into the sprayer-works like a charm. Your sprayer may have a screen through which you pour fluid. This would filter out large debris. What debris does get through tends to get stuck in the spray tip. See if your spray tip will unscrew for cleaning.
When done using the sprayer for the day, be sure to wash it out, including the spray wand. The microbes are alive and can grow to clog the thing up overnight.
Seed the Mind, Harvest Ideas.
a towel is quite possibly too tight to allow fungal hyphae to pass, which are critically important for perennials. Tim Wilson @ microbeorganics.com has done studies on this, his webpage will probably have the minimum micron measure needed to allow the fungii to pass.
Personally I have given up on the sprayer for applying compost tea to my apples. I just use a small bucket and throw on one bucket per tree in a careful sweeping motion. I can throw the water a lot higher than my sprayer can spray. Just practice with regular water for a while to refine your technique.