There are neurotransmitters that are associated with specific functions within a neural circuit, but I would not associate a specific neurotransmitter with a specific sensation. There is also more complexity to this, because there is a plenty of receptors for each neurotransmitter. These receptors have slightly different properties, which may influence the effect on the post-synaptic neuron and consequently the percept.
Another concept is the effect of neuromodulators that regulate larger areas of the brain, e.g. noradrenaline, or serotonin. These have broad effects that change the brain state and are associated with a certain 'feeling'. For example, release of noradrenaline would lead to higher ventilation, higher heart rate, sweating etc.