I was accused of theft by a supermarket. The manager apologised to me but they’ve refused to pay me compensation.
If the store had no reasonable grounds for detaining you and you were held against your will you may be able to claim compensation for false imprisonment but you would have to prove it. Usually a store detective will say that you agreed to be detained. You might also have a case if, for example, you lost your job because of the stain on your good character. If the accusation caused more than just hurt feelings and was overheard by others you may have a claim for slander but it would be an expensive case and you would have to show that the accusation caused serious damage to your reputation.