It's true that the 2 isues are closely related. But you have your facts wrong. The data show clearly that decline started before 1968, and it was already in full bloom by the time Humanae Vitae was released. Long before Humanae Vitae, the New Mass in the vernacular and the other changes associated with Vatican II had started to drive away a large proportion of the Catholic population.
Besides the statistics, look at it from a spiritual point of view: How was it possible for bishops, priests and lay people publicly to deny and dissent from an essential Catholic doctrine? Only someone who had already fallen from a state of grace could do so. The reaction to Humanae Vitae could never and would never have occurred prior to Vatican II.