What sort of fence were you painting and what sort of paint were you using ? Are the concrete posts already painted or just bare concrete ?
The type of paint used is needed so we know will dissolve it (hot soapy water for fresh emulsion, turps for gloss paint etc) and if the posts have previously been painted, then you will need to be very careful if you use turps or white spirit. You might be able to just use soapy water with a stiff wire brush or a scrubbing brush on fresh emulsion or creosote - in other words elbow grease ! Can you post a picture of the splattered post ?