Try a combination of white vinegar and scraping. The vinegar will soften the concrete a little allowing it to be scraped. The vinegar can be applied with a spray bottle or brushed.
It will take about 30 minutes for any reactions to start. Keep the concrete splashes wet during and after this time, then check it with the paint scraper or stiff putty knife. If you don't want to scrape, try using a small stiff nylon scrub brush instead. Using a scrub brush will be slower and more labor intensive.
Make sure to protect your patio from drips of pure vinegar as this will cause spots on your concrete. When the concrete splatters are removed, rinse the area(s) well with a garden hose and prime when dry.