Sounds like it was an heat-seaking SAM. Stay above 10,000 Feet to avoid them.
You have one option with the RWR; "Change RWR/SPO mode". This Filters out anything that is tracking you and will only show you contacts which have locked you and active radar homing missles (aim-120, r-77). So if you are not in combat, it will appear that your RWR is off.