Sign in, copy your group's URL, and POST to it from a script, a cron job or your monitoring. Everyone in the group gets a push. Ack silences it for the group; Close ends it.
curl -X POST 'https://api.zapapush.com/hooks/send?key=YOUR_KEY' \
-H 'Content-Type: application/json' \
-d '{"subject":"Disk full","description":"/var is 95% used"}'