I think there is not enough communication with the public. Paradoxically when advertising that CERN has found the Higgs Boson, the average Joe cannot directly see why there is value in that discovery, but when you advertise that CERN has developed the World Wide Web and gifted it to humanity BECAUSE it was working on particle physics, the average Joe can understand the value of working on particle physics and hopefully he will support the development of scientific projects in the future.
When putting things into prospective, CERN costs are nothing compared to the priceless innovations coming out of it (and you know that better than me for sure).