Not sure about feedback inhibition (you mean negative feedback, of the kind done by autoreceptors like a2 adrenoreceptors or 5HT2a?)
But with allosteric regulation, you have two or more active sites on a receptor, the main agonist binding site, and one, or more, allosteric sites, a direct agonist/antagonist/inverse agonist binds to the main active site and does whatever it does at that receptor, opens/blocks/closes ion channels, activating second messengers and all that.
Direct agonists will cause a change in the activity of the receptor equal to their efficacy at that receptor, whilst an allosteric modulator binds to the allosteric site(s) and on its own, in the absence of a ligand bound to the main active site will cause no activity at the receptor, but when bound in the presence of a direct agonist will increase the maginitude of the response in the case of an positive modulator, and in the case of a negative modulator, decrease it, through indirect mechanisms such as changing the conformation of the receptor to one that binds with greater efficacy/affinity to the main binding site.
A good example would be the GABAa receptor.
The endogenous ligand is gamma-aminobutyric acid, GABA, which acts to open the ion channel, and pass chloride currents, decreasing general neuronal excitability, as its the main inhibitory neurotransmitter, the common sedative drugs of the benzodiazepine family bind to an allosteric site, changing the conformation of the receptor to one that binds with much higher efficacy to GABA, which in turn, causes an increased maximal stimulation of the receptor compared with that of GABA alone.
Different allosteric modulators can have different effects on channel conductance of course, with the benzodiazepines serving to increase channel opening frequency, whilst the far more dangerous barbiturates are also allosteric positive modulators at a different binding site, and both cause the ion channel to open more frequently, but to increase mean duration of the open state.