I assume littering is partially cultural (not everyone is raised to think littering is wrong) and also partially about opportunity (what reasonable alternatives did people have for waste disposal).
In terms of culture, you have to get them while they're young, with propaganda designed for children, like Mr. Rogers or Sesame Street.
In terms of opportunity: maybe when ordering a new drink, people are running out of free cup holders in their car and need to dispose of their morning coffee cup to make room for the new drink they just ordered, so making a trashcan available might make the most sense to reduce littering.
Sure, we can feel anger towards the individual litterbug (probably some of them know it's "wrong" to litter and could do more to avoid the need to litter - personally I would empty the liquid and then keep the trash cup in a plastic bag I keep for trash in the car), but it's more practical to address this as a social problem.