The ZAFU is the round cushion used in Japan as an aid in helping one to ease into sitting cross-legged on the ground. When one is accustomed to that posture, then he can progress to the half-lotus position, then to the full-lotus. As the zafu is an aid, so sitting in itself is just another aid to a relaxed posture, a balanced body, relatively unmoving, with the backbone straight, and thus sitting is an aid to meditation. Likewise, meditation aids one to concentrate and focus the mind inside so that the Dharma can be understood and practiced.
The abbot of the Berkeley Buddhist Monastery, the Venerable Heng Sure, tells a story (if I remember it correctly) of how he was accustomed to meditating on a zafu for many years, when one day he was suddenly surprised by Master Hua who yanked the zafu out from under him. Now without the support of the zafu, Heng Sure plopped flat on the ground. Master Hua explained that one is much better off not relying on a prop, because, though it was useful in learning to meditate, if Heng Sure could learn to sit without it, he would gain benefit in two ways. First, he would be free of the need for this prop, and second, he would be able to meditate anywhere.
This same lesson applies to those who use beads to count mantras. The beads are just an aid, likewise mantras are just an aid. So though beads are very useful in learning to count mantras, and in unifying body-speech-and-mind, there are times when the use of beads is not practical, or not possible, or an obstruction; or there are times when one is not in possession of a set of beads. In these cases, assuming one has already completed millions of repetitions, one should learn other techniques for counting mantras, such as with the fingers (using the opposable thumb and the joints of the fingers), or by placing each repetition at a different point in the body, or outside the body, etc.