This is not correct. In an extreme case, if there is only 1 left unvaccinated, the disease won't spread. If there are two left unvaccinated, the chances of one having the disease and the other being initially uninfected and then subsequently infected by the one possible vector is astonishingly small.
In reality, for a vaccine to be effective, the portion of the population that needs to receive that vaccination is significantly less than 100%.
Moreover, vaccines based on attenuated vaccines (e.g., the polio vaccine) actually infect the recipient with an impotent version of the virus. This virus will be transmitted to others in the community through normal contact, thus conferring immunity to many that did not receive the vaccination directly.
(this isn't intended to be an endorsement of those who refuse to get vaccinated)