Some schools are a lot stricter than others, but it's still possible to get into a good CACREP-accredited program without having a degree in anything psychology-related. Schools who are more lenient will at least require that you have taken a certain number of psychology courses in your undergrad (or will specify certain pre-reqs that you can take before matriculation)... while some may even just take people with no background at all on a case by case basis.
One thing that might help you out a bit is to do some volunteering with a local mental health agency, community counseling service, group home, etc. Office work, fund raising, working on a crisis hot line... anything that will give you some exposure to counseling/mental health and will show schools that you're interested. Or... get a job at a residential home! Many just want someone there to make sure the residents are taken care of/don't escape. Some of my class mates have done or are currently doing this. One in particular has his undergrad in business...
I also recommend doing some heavy internet research to see what you can find out and start talking to schools that you think look interesting. If you want to help people and are interested in psychology/counseling... we (as in everyone) definitely need more people like you in the field! By that, I mean people who are willing to grow outside of their normal area of focus.
Anyway... let us know what you find out. I am sure there are a lot of people here who can offer you some good pointers.