What is the antagonist of epinephrine?
You should understand that it is not the neurotransmitter that is responsible for an effect; it is the neural network that causes an effect and the neurotransmitter is just a mediator. 

In CNS, glutamate is generally used in excitatory synapses whereas GABA is chiefly used in inhibitory synapses. Similarly, in peripheral nervous system epinephrine and acetylcholine are used in excitatory synapses whereas glycine is used in inhibitory synapses. Some neurotransmitters always cause excitation in the post-synaptic cell (for example glutamate), however, they can also cause activation of inhibitory neurons and thereby cause inactivation, indirectly. Also, the post-synaptic effect depends on the type of receptor expressed by the post synaptic cell and not the neurotransmitter per-se. For example, α-adrenergic receptors cause smooth muscle contraction whereas the β2- receptors cause smooth muscle relaxation [1]. Similarly, there are both inhibitory and excitatory dopamine receptors [2].

The two divisions of the autonomic nervous system — the sympathetic and parasympathetic systems act in a complementary manner. The former uses epinephrine and norepinephrine whereas the latter uses acetylcholine.