The concept of time, or more importantly the feeling of a distinct lack of it, is a completely fabricated one. The measure of time is something that has been thrust upon us, and one that we collectively choose to buy into.
The animals are aware of the movement of time by the movement of the sun, but one would be hard pressed to say that this made them anxious and stressed. What cannot be done today just gets done tomorrow.
Without descending into a complete state of chaos we can apply this to our own lives by appreciating the moment we find ourselves in.