The footage, shared publicly by Dorset Animal Action, appeared to show a goat being dragged along a roadside by its collars before being moved into a pen.
The charity has called for a wider ban on live animal displays at public events, saying such attractions are stressful and unfair on animals.
The goats are a familiar sight on Bournemouth’s cliffs, where they are used as part of a conservation grazing scheme.
Jackson accepted it was “not an acceptable way to move the animals around” and said the welfare of the goats is his top priority.